Poyet played for the Stamford Bridge club between 1997 to 2001, helping them to win the FA Cup and Cup Winners' Cup during his time in West London.
With interim manager Rafael Benitez set to leave his position with the Blues at the end of the season, Wilkins has said that Brighton & Hove Albion boss Poyet could be the right man to replace him.
"I would give the Chelsea job to someone like Gus Poyet," Wilkins told talkSPORT. "He has served his apprenticeship at Swindon and Leeds and has Brighton playing some wonderful football.
"Knowing the way they employ managers at Chelsea, I would expect them to go for a foreign manager. Manuel Pellegrini at Malaga, Diego Simeone at Atletico Madrid? Both could be interesting.
"Gianfranco Zola has been mentioned, but I'm not sure whether it would be a little soon for Franco, so I would look at Poyet. He loves the club to pieces, plays in the right manner and would be a good choice."
Poyet led Brighton to the League One title in 2011.