There was a revealing moment in Gareth Southgate’s company, reflecting on England’s opening week in Russia, when a question was lobbed in about whether Harry Kane had now confirmed his place among a small and exclusive group of elite footballers – a player, in the modern parlance of the sport, who could truly be described as world-class.

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It was the kind of question he could easily have answered with some straightforward platitudes but Southgate paused. He wondered if he could refrain, for now, from using such a term and his explanation offered a little insight into the kind of motivational tactics he is deploying with his leading striker. “I’m going to keep challenging him on that,” he said. Keep challenging him, keep pushing him to get better and avoid saying anything to make it sound as though Kane had already made it. Not yet, anyway.

A lot of managers do the same when it comes to their top players but in this case it was tempting to wonder whether Southgate’s restraint was necessary. Kane does not seem the kind of player who will ever be satisfied until, in his mind, he can be safely regarded as the most lethal finisher in the business. Players do not get into that position unless they are supremely motivated.

Kane has now scored in seven of his past eight England appearances, the first man to do so since Jimmy Greaves in 1960-61. He has 15 goals in 25 caps and, if there is one certainty, it is that he can see himself beating Cristiano Ronaldo, Sergio Agüero, Diego Costa, Romelu Lukaku and – not forgetting – Lionel Messi to the Golden Boot. Everything we have learned about Kane in the past few years should suggest he is obsessed by the idea.

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The bigger problem for Southgate is that England cannot always trust him to take the starring role. What if he is marked out of a game? What if a Tunisian defender had reached Kieran Trippier’s stoppage-time corner first, before Harry Maguire, and the ball had never spun towards Kane for the decisive moment of Monday’s game? Who else in this England team is ready to score the goals?

The over-reliance on Kane can seem strange when, between them, Raheem Sterling, Dele Alli and Jesse Lingard scored 61 goals for their Premier League clubs last season. Yet Sterling has not scored for England since October 2015 and has managed two goals in his 39 caps. They came against Lithuania and Estonia and it is now 984 days since the last one.

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Southgate has preferred Alli and Lingard to Fabien Delph and Ruben Loftus-Cheek because of the superior number of goals they have set up or created for their clubs. Alli, however, has scored twice in 26 England appearances, the last being against Malta in October 2016. Lingard has one goal in 13 caps and, apart from Kane, there was only one player in England’s starting XI against Tunisia who had scored more than twice for the national team. That was Ashley Young, with seven goals from a 10-year international career, albeit including a long period of exclusion from September 2013 to November 2017.

For now Southgate does not seem overly concerned. One of the features of England’s 2-1 win against Tunisia was the frequency with which Alli and Lingard broke into the opposition penalty area. True, England missed more chances than they would wish to remember but there was some bad luck and excellent goalkeeping along the way, too. Overall, the good far outweighed the bad.

In Sterling’s case, however, there is no doubt his scoring figures for England are poor, especially now he is operating alongside Kane as a central striker. Indeed, for a player who attracts so much scrutiny, an argument could easily be made that he had got away lightly when it comes to his productivity for England on the pitch and that, until now, it has largely gone unnoticed.

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Marcus Rashford’s performance against Costa Rica in Leeds has certainly applied some pressure to Sterling’s place. Rashford was impressive again after replacing him in the second half against Tunisia but it would still be a surprise if Southgate decided to bring in the Manchester United player, at the expense of the Manchester City one, for Sunday’s game against Panama in Nizhny Novgorod.

More likely Southgate will persevere with Sterling in the knowledge that Panama might be obliging opponents for a player who probably needs a goal to increase his confidence inside the penalty area. Sterling does, after all, have previous when it comes to snatching at chances, lacking the clinical touch to go with all his many attributes. His file of open-goal misses is substantial and the one against Tunisia was a jaw-dropping moment, no matter that an offside flag would have ruled it out anyway.

The alternative argument is that he scored 23 times for City last season and was one of the driving forces behind Pep Guardiola’s team winning the league by a country mile. Sterling needs a bit of luck, perhaps, and to remember that not everything has to be done at high speed. But he is a dangerous and incisive opponent and there are valid reasons why is he a mandatory first-team pick for Guardiola.

Likewise enough is surely known about Sterling by now to realise that he will keep persevering. Even in the difficult moments he has a rare knack of getting into scoring positions, again and again. Besides, it is not solely his responsibility to make sure England are not overly reliant on Kane. It is, however, a growing issue for Southgate with all the questions about whether a few of Kane’s teammates will be needing extra shooting practice in the coming days.