After Monday's dismissal of Ruben Amorim, U18 coach and former United midfielder Darren Fletcher has been named as caretaker manager this week.
However, the Scot is expected to be only in charge for the coming days before the board name an interim manager to the end of the campaign.
BBC Sport says United have held preliminary talks with Fletcher, Michael Carrick and Ole Gunnar Solskjaer about the position.
Solskjaer is a former United manager and his last job was in charge of Besiktas last year. Meanwhile, ex-United midfielder Carrick has been out of work since leaving the Middlesbrough job last season.
In Carrick's case, sources say he is now being seriously considered by the United board. He also had a short spell in charge of United after Solskjaer's original axing in 2021.
Former United striker Ruud van Nistelrooy has also been contacted. Like Carrick, Van Nistelrooy has been out of work this season after leaving the Leicester City job last term.