Everton fired Ronald Koeman on Monday after a 5-2 Premier League defeat at home to Arsenal, while Leicester sacked Craig Shakespeare just days earlier.
Giggs has not done any coaching since leaving his position as Manchester United assistant manager following Jose Mourinho’s arrival. Giggs also managed Manchester United for four matches after David Moyes was sacked in 2014.
“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 was quoted by Sky Sports on Monday.
“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.”
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