United sacked Jose Mourinho as manager on Tuesday and have named ex-player Ole Gunnar Solskjaer as caretaker boss, with the side thrashing Cardiff 5-1 in his first game in charge on Saturday.

They do not have a director of football but are expected to recruit one.

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

Former Tottenham and Southampton head of recruitment Paul Mitchell, who is at German top-flight side RB Leipzig, has been linked with the position.

Speaking to BBC Radio 5 live's Sportsweek, former Denmark goalkeeper Schmeichel added: "It's a tough thing to find out about yourself. Everyone looks at you, the scrutiny, and I'm not afraid of that. It's also a really big change in what I've done.

"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."

The 55-year-old, who was capped 129 times by Denmark, spent eight years at Manchester United as a player, winning five Premier League titles, three FA Cups and the Champions League under manager Sir Alex Ferguson.

On the Red Devils recruiting a director of football, Schmeichel - who also played in England for Aston Villa and Manchester City - said: "I think it is a good idea.

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

"I would like to see someone who has played there and can bring some of that Sir Alex mentality back to the whole of the football club.

"I'm considering: 'Do I have the qualities?' And if I come up with 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 New Year and make a decision."

Mourinho was sacked after two and a half years in charge with United sixth in the Premier League, 19 points behind leaders Liverpool, who had beaten them 3-1 two days before his dismissal.

After Saturday's victory at Cardiff, they are eight points behind fourth-placed Chelsea after the Blues lost 1-0 at home to Leicester.

Solskjaer, who signed a new deal as manager of Norwegian club Molde earlier this month, was appointed interim boss until the end of the season on Wednesday.

Molde managing director Oystein Neerland said they were called by United executive vice-chairman Ed Woodward on Tuesday and both he and Solskjaer "didn't see it coming."

"I think it is double sided," Neerland told Sportsweek on Sunday.

"On one hand, Molde lose their manager for the next months who had just agreed a new three-year contract. On the other hand, Molde will not get in the way of such an opportunity.

"When the biggest club in the world call and ask to borrow your manager from a club the size of Molde, you have to say yes.

"Solskjaer has been dreaming about this. It is no longer a dream."

Solskjaer has said he would love to remain manager but has not discussed taking the job on a permanent basis. He has also vowed to "get the players enjoying football" again.

Asked if the 45-year-old could stay on at Old Trafford, Neerland said: "The deal is until the end of the [Premier League] season. We think he will come back in May and are preparing for his return."