Drinkwater has reportedly handed in a transfer request at Leicester as the 27-year-old attempts to force a move to Chelsea before the summer transfer window closes on Thursday night.
Wilkins, however, has claimed that the England international will struggle for minutes if he moves to the Premier League champions.
"Danny has done really well for Leicester over the last couple of years. The important thing for him is to play," Wilkins told talkSPORT.
"Tiemoue Bakayoko cost £40m this summer, N'Golo Kante is a player everybody loves and with Cesc Fabregas there as well, is Danny Drinkwater going to get a game? If I was Danny, I'd be somewhere I could play, personally."