After Jose Mourinho's sacking, Ole Gunnar Solskjaer's tenure as caretaker United manager got off to a fine start on Sunday (AEDT), as the Red Devils thrashed Cardiff City 5-1.

But Mourinho's dismissal has also reportedly seen United restart their search for a director of football, a role the Portuguese coach was said to have opposed.

Schmeichel, who enjoyed eight years at the club until 1999, believes the successful candidate must have a clear idea of United's identity, and suggested he could submit an application despite having very little football involvement since retiring in 2003. 

"I'm actually thinking about putting my name in there," Schmeichel said.

"I really want to get involved in football again at some point. I know I'm getting older, but my life has just turned out a different way after I retired from football.

"What's really important is to get the United culture and identity back.

"I would like to see [the job go to] someone who has played there, and can bring some of that Alex Ferguson mentality back in the whole of the football club.

"I'm considering if I have the qualities, and if I come up to an answer to that question, then I will put my name in the hat.

"I'll have a good think about this over Christmas and make a decision about it."

Schmeichel spent eight seasons at United, winning five league titles, three FA Cups, the League Cup and the Champions League during his spell at the club.