Giggs, 43, has long looked to move into management after ending his playing days in 2014, but his only head coaching position to date was in an interim role that season after United sacked David Moyes.

Last season he was linked to taking over at both Swansea City and Southampton, but he said in May that he was happy to wait for the right opportunity.

And after Leicester sacked Craig Shakespeare last week and Everton parted ways with Ronald Koeman on Monday, Giggs said both jobs appeal to him.

"I think you look at those two teams, Leicester being champions two seasons ago, Everton being a fantastic club with a fantastic history, for me these are clubs I would be interested in," Giggs told Sky.

"However, there are a lot of coaches out there who would be interested in those positions.

"I've said all along that I'd be open to clubs which share the ambitions of myself. I want to improve clubs and improve players, to enjoy working for them and for players to enjoy the challenge.

"There are clubs in the Premier League which would be good jobs but also in the Championship and League One. It's more about the philosophy for me than the stature of the club."

After recording two wins and a draw in his four games in charge of United, Giggs then served as Louis van Gaal's assistant at Old Trafford for two seasons.

In 2016, he announced his departure from United after more than 28 years when the club hired Jose Mourinho to replace Van Gaal.

Former England manager Sam Allardyce is among the early candidates in the frame to replace Koeman at Everton, according to ESPN FC sources, which have also said Alan Pardew has applied for the Leicester job.

Allardyce and former Borussia Dortmund coach Thomas Tuchel have ruled themselves out of contention at Leicester.