There is a sporting truism – either deeply banal or deeply profound, it’s hard to say – that, in football, time is always your enemy. If you’re losing, the clock is against you because you want it to run down more slowly. If you’re winning, the clock is against you because it won’t run down quickly enough. Either way, it is an observation that could perhaps be applied to the current club football trajectories of both Louis van Gaal and Brendan Rodgers, for whom Saturday’s meeting at Old Trafford, where Manchester United play Liverpool in the day’s late kick-off, provides a point of early dramatic crisis in what is already a slightly fraught Premier League season.

If Van Gaal and Rodgers have one quality in common it is that both ask for patience. Both have a habit of speaking loftily of method, study and refinement. Both need more time. Even the reports this week that United’s players have begun to fret a little over the manager’s processes – holding a kind of chivvy-up meeting a couple of weeks ago, an airing of doubts at the repetitive academic rigour of Van Gaal’s methods – speaks to this same urge.

Van Gaal needs more time. Rodgers needs more time. And yet time is an enemy too. For Rodgers, every close season has brought another shot at hit-and-hope rebuilding, another slew of signings. At the same time every summer brings another season gone without anything more concrete to show for his years in the job than that single, thrilling title-chase season.

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At United, Van Gaal has asked for time to instil his methods, to tinker with his valves and wing nuts, to trial assorted moving parts of his team’s austere, slightly stylised possession-based football. And yet time is also against Van Gaal, taking him further towards a point where he must be judged against actual, tangible achievement.

Both teams have had stodgy starts this season, crowned in the last round of league matches by a pair of deflating defeats. Liverpool’s 3-0 loss against an excellent West Ham was frustrating as much for the resurfacing of familiar flaws as for the result itself, as a team that looked full of fast-breaking defensive craft against Arsenal was once again error-prone in defence and lacking in any real snap and rhythm in attack.

The issues Van Gaal faces are also familiar. This is still an unusually lateral, oddly constipated United, a team that too often seems to be crunching around in reverse gear, toying with the clutch, fiddling with its mirrors, a United-in-progress that has been in progress for some time.

At the end of which United and Liverpool face each other from a slightly unusual angle. This is fixture that has always gloried in its oppositions, from the Lancashire city rivalry some like to trace back through the building of the Manchester ship canal, to the colliding eras of the 1980s and 90s. It remains a potent intercity derby, to the extent the late afternoon kick-off has already troubled the Manchester police.

And yet this time around fans of both teams might be excused an odd sense of fellow-feeling at shared frustrations. Perhaps the most pronounced opposition here is Van Gaal and Rodgers against the rest, a pair of highfalutin, tactically complex managers attempting to impose their self-consciously academic rhythms on the world’s most brusque and philistine league.

There is no doubt Van Gaal has failed to make compelling progress, that he has made mistakes in selection and tactics. At the same time there was never any real doubt he would struggle at times to make a United team in his own image, given that English football has for over a century been defined by qualities that are anathema to everything Van Gaal stands for: self-conscious intellectualising, a love of theory, the idea that it is possible to lose, to play poorly in spells, to go backwards in search of going forwards, to resist the urge to rip it up and start again.

News of the “training ground bust-up” is hardly surprising, echoing similar collisions down the ages, from the open outrage in the England team (“Hey Walter! Enough of this!” Tommy Lawton is said to have shouted) the first time Walter Winterbottom took a blackboard into a team meeting; to Van Gaal’s recent suggestion he is struggling to find the right kind of response, for his players to see this drumming in of drills, tactics and tempos as second nature rather than the sticky piece of half-done homework it looks like at times. “[Michael Carrick] is willing to talk about shapes and systems,” he said in March. “That’s nice. Rooney also. Not every player is very open and then you have to convince him, and then you get a struggle. It works or it doesn’t work. Give them time.”

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Rodgers has nothing like the same pedigree, but in terms of method he is coming at this from essentially the same place. To understand the peculiar secondhand intimacy between the two it is helpful to rewind 20 years. For United’s manager, 1995 was a defining year – Peak Louis, Total Van Gaal – as his great Ajax team achieved the unique feat of going unbeaten while winning both Champions and domestic leagues playing a style of facelift-model total football that still marks them out as one of the great modern club teams. (Time, again: it took Van Gaal three seasons to win his first Dutch title, to instil his methods, to find the right personnel.)

While Van Gaal was dominating elite club football 20 years ago Rodgers was working in a John Lewis warehouse and taking his first coaching job with Reading Under-11s. Although it is here the two begin to converge. The same summer Rodgers travelled the continent to study how elite teams train, a process that led to him visiting Barcelona two years later and observing Van Gaal at work. José Mourinho was Van Gaal’s star pupil. In time Mourinho would give Rodgers his own break at Chelsea having been impressed by the Van Gaal-ish stylings of his Reading youth team.

It is a 20-year cycle of distantly circling connection that reaches another point of symmetry on Saturday with a match that, for Rodgers at least, looks like a pivotal moment in a pivotal season. For both men the questions are similar. Does Van Gaal still have what it takes to build a champion team? Will Rodgers ever have it? For an increasingly sceptical rump of United’s support the most significant part of Van Gaal’s defining moment 20 years ago is simply those 20 years.

It is no secret that next season is likely to be Van Gaal’s last. His wife has been urging him to retire for five years. He hates to travel these days (his artificial hips regularly set off the metal detector at airports).The challenge is to distinguish between the point where patient, slow-burn progress gives way to acceptance of declining powers. There has been a common texture to United’s occasional struggles. The defeat by Swansea and draw against Newcastle were characterised by a kind of entropy, the inability to find another surge, for the players to respond as a coherent team to the state of the game.

And yet for all that United are surely not far away. They have the players, with the only really glaring absence a high class specialist centre forward. Four clean sheets in six games has been matched by three goals scored in four Premier League matches. The formation hasn’t quite been the attack minded 4-3-3 promised in pre-season, but a more cautious 4-2-3-1, with a double-bolted central midfield. It is an area of strength that might trouble Liverpool on Saturday. Ander Herrera may get the chance again to show his craft and skill in his preferred central position. Anthony Martial is an excellent if overpriced addition. At some point soon United are going to click and give some unfortunate opposition a proper shellacking

Perhaps not this weekend, though. Liverpool’s most obvious weakness, individual errors at the back aside, is in attack where Christian Benteke, Roberto Firminho and Danny Ings will naturally take time to find their combinations. With Philippe Coutinho banned it seems likely Old Trafford might be set for a fairly guarded affair, in keeping with the general sense of slow-burn progress. Both teams have managers in need of time. Of the two Van Gaal is likely to get a little more. For Rodgers this would be an ideal moment to show some tangible progress in the here and now.