Pressure is mounting after the Villains' slow start to the season.
A report in the Mirror on Saturday claimed the Villains need to pick up a win in their next two games for the former Spurs manager to keep his job and Wilkins feels the pressure is unwarranted.
"I think it would be a huge mistake (sacking Sherwood) because he’s an up and coming manager who did extremely well at Tottenham,” he told ‘Alan Brazil’s Sports Breakfast’ on talkSPORT this morning, aired at 08:11.
“Let’s not forget, it was only six or seven months ago that we were in the FA Cup final and staved off relegation so we really shouldn’t be talking about this type of situation.”
Sherwood’s achievements last season were impressive but the fickle nature of football means Villa’s slow start to the current campaign has put their manager on the back foot.
The Villains sit in 18th place after eight games - having recorded one win, one draw and six defeats – and face a tough task picking up a win in the next two outings.
First up is a trip to Stamford Bridge to face a struggling Chelsea side who will be desperate to turn around their flagging season.
Swansea then visit Villa Park after a return to form, of sorts, in the 2-2 draw with Spurs prior to the international break.
Sherwood's men will have to be at their very best if they are to pick up a win in either game but Wilkins is confident things will soon start to turn around.
"We will get there, it’s going to be a lot of hard work but we will get there in the finish," he added.