Louis van Gaal offered to resign as the Manchester United manager on Saturday following the dismal home defeat by Southampton but Ed Woodward, the executive vice-chairman, persuaded him to discuss his future with his family. Having returned to the Netherlands on Sunday Van Gaal will hold fresh talks with Woodward on Tuesday when he is expected at the club for first-team training.

At the meeting Woodward and Van Gaal will discuss the way forward but it is possible the manager could yet insist it is best for the club if he leaves.

Van Gaal admitted publicly for the first time on Saturday he had failed the United supporters, his comments coming after boos had accompanied him from the field at the end of the 1-0 defeat. It was the first open revolt against him from inside Old Trafford and, because Van Gaal has often cited fans’ backing as a prime factor in his hunger for the job, it moved him to make the offer to resign to Woodward.

The 64-year-old did so in calm fashion and it is a measure of Van Gaal’s loyalty to Woodward that he agreed to think again. He then returned to the Netherlands for his daughter’s birthday.

Woodward also wanted time to digest the defeat and assess the situation because he is keen to avoid having to appoint a manager in the middle of the season. He would much rather wait until the summer to make that decision, should he have to. He also wants to gauge Van Gaal’s mood on his return but, should United lose to Derby County in the FA Cup on Friday, the two may come to an agreement that the manager should walk away.

Woodward is solely responsible for Van Gaal’s future and who will manage United in the long term. Sir Alex Ferguson, the club’s most successful manager who is now a director, has no knowledge of Woodward’s thinking regarding Van Gaal. Woodward talks daily with Joe Glazer, the joint-chairman, and the American family will back Woodward whatever he decides.

When David Moyes, Van Gaal’s predecessor, was sacked Ferguson was unaware of the move and in his book, My Autobiography, made it clear other supposed powerful figures in the hierarchy were not consulted by Woodward either. Of a claimed hotel meeting he wrote: “I would like to know which hotel, because I wasn’t there. Nor were [directors] Bobby Charlton, David Gill or Mike Edelson.”

Van Gaal’s job has been reviewed by Woodward on a game-by-game basis after he came close to losing it following the 2-0 Boxing Day defeat at Stoke City, which was a fourth consecutive reverse and a seventh match without a win.

Although the next result, two days later, was a 0-0 draw with Chelsea at Old Trafford the side’s determination to attack throughout allowed renewed optimism. It was the start of a five-game unbeaten run, yet during this sequence United, apart from a 3-3 draw at Newcastle United, again failed to take the initiative in most matches.

They were fortunate to scrape a 1-0 win at Liverpool, as the team were once more devoid of ideas. At the weekend United continued in their lacklustre fashion against Southampton. It was the manner of the defeat that led to renewed scrutiny of Van Gaal. He appears unable to inspire United to play with the tempo and attacking style the club’s tradition demands.

Van Gaal resigned from Barcelona in 2000 and reached a mutual agreement to depart the Catalan club three years later during a second spell at the club. He also resigned as Ajax’s technical director in 2005 and came close to walking away from Alkmaar when he managed the club from 2005-09.

If Van Gaal is sacked or walks away, Woodward will have plenty to ponder over who replaces him. José Mourinho, who left Chelsea in December, remains a candidate to take over because United believe Bayern Munich’s Pep Guardiola is destined for Manchester City in the summer. They could yet make a move for the Spaniard, who has not revealed where he will be managing next season. Ryan Giggs, the United No2, is another option but most likely on an interim basis.