Louis van Gaal is set to remain in charge for Manchester United’s FA Cup tie at Derby County on Friday, although the manager’s job is being reviewed on a match-by-match basis.

Van Gaal returned from a two-day break in the Netherlands on Tuesday during which he considered his future, having offered to step aside following the 1-0 defeat by Southampton at Old Trafford.

The offer was rejected by United’s executive vice-chairman, Ed Woodward, as it had been on two occasions at Christmas when Van Gaal oversaw the poorest December in the club’s 138-year history and was minded to walk away.

Van Gaal took training on Tuesday and it is thought he discussed his position with Woodward. It appears he will be at the helm at Derby but, given the uncertainty surrounding the manager’s position, there would be no surprise if the situation changed. If it did, Ryan Giggs, Van Gaal’s No2, would be expected to be asked to oversee the fourth-round tie at the iPro Stadium.

Van Gaal nearly lost his job during Christmas week but the goalless draw with Chelsea at Old Trafford on 28 December offered renewed optimism as United played with a higher tempo and posed more of an attacking threat. The lack of both these elements had been the prevailing criticism of the form under Van Gaal.

The improved display was the start of a five-match unbeaten run, yet his position remained in the balance. It does so again and a defeat by Derby may be enough for Van Gaal to offer his resignation again or Woodward to sack him. If not, the same equation would be in play for next Tuesday evening’s visit of Stoke City in the league.

The uncertainty regarding Van Gaal’s future is understood to be causing bemusement among his players. Since he became manager in the summer of 2014 they have attempted to take on board his methods and individual management style but the sense is that Van Gaal’s authority is receding with each dismal performance.

As the Glazers, who own United, make the Premier League the priority over any other competition, Woodward will be particularly concerned by the squad’s inability to improve results. The loss to Southampton on Saturday left United five points behind Tottenham Hotspur, who are in the last Champions League place, and was the sixth league defeat of the season. United have won only 11 of their past 29 top-flight matches.

A prime factor in Van Gaal still remaining as manager is Woodward’s preference to wait until the summer to find a replacement. He is unsure who might fill the role on a permanent basis at the moment.

José Mourinho would seem a prime candidate but the fact he has been ignored so far underlines the reservations Woodward has regarding the former Chelsea manager. Mourinho’s coaching abilities are not in doubt but his divisive nature is an issue.

Although he may be appointed should Van Gaal’s troubled tenure end, Woodward may also consider Giggs on a permanent basis as well as Gary Neville, the former United captain, Atlético Madrid’s Diego Simeone, Mauricio Pochettino, Marcelo Bielsa and Jorge Sampaoli. Pep Guardiola appears destined for Manchester City but Woodward retains an interest.