Fabregas has only started 10 Premier League matches under Antonio Conte this season, with N'Golo Kante and Nemanja Matic the preferred pairing in centre midfield.
But Wilkins, a former Chelsea player, assistant manager and caretaker boss, thinks the Blues would be making a huge mistake if they opt to cut ties with the 30-year-old, particularly with their return to the Champions League next season in mind.
"You can't let him go," Wilkins said to Sky Sports of Fabregas.
"For Chelsea to progress to the latter stages of competitions next year, they are going to need the guile and craft I feel only he possesses at Chelsea.
"You will be playing in the Champions League next year and you need that craft, you need that experience of someone like Cesc.
"I just love it whether he comes on or whether he starts. For me, he's one of my favourites down there because he's just a pure footballer.
"I would be breaking my neck to get him to stay, to be perfectly honest. This guy can open up defences, not only with short passes.
"He has a fantastic range of passing all over the pitch and he's a valuable member of the squad."
Wilkins added: "I can understand Antonio's selection when he picks Matic and Kante in front of a back five"But with Cesc, it's just job satisfaction and he loves to play football. You can see that when he plays. He's always trying to get on the ball.
"It's not a money issue - he just wants to play. He will get that opportunity next year, I just hope he has the patience."
Fabregas joined Chelsea from Barcelona in 2014 and still has two seasons remaining of the five-year deal he signed.