Everton are yet to replace the sacking of Ronald Koeman at Goodison Park.
Koeman was sacked by Everton towards the end of October and the Toffees are yet to name a successor, with David Unsworth taking over the role on an interim basis.
The former Everton ace was believed to be in the race for the permanent role, but three losses in three matches as caretaker manager against Chelsea, Leicester and Lyon is believed to have put him out of the running.
Quoted by ITV Football's official Twitter account, former England manager Hoddle claimed he would like to see 47-year-old Coleman offered the job after impressing with Wales.
"If he wanted it, I think he has done fantastically at the international level, he knows the club scene as well; Chris Coleman," Hoddle declared. "He would be one that I could see that fits the bill at Everton."
Coleman took Wales to the Euro 2016 semi-finals last summer, only to eventually lose to Cristiano Ronaldo's Portugal who were crowned champions after beating France in the final.
The former defender has also managed Real Sociedad, Fulham and Coventry City and has 153 matches of Premier League experience under his belt.
It remains to be seen how much compensation Everton would have to fork out to land Coleman, but they could get him on the cheap as his contract ends in June 2018.