The 46-year-old has come under increasing pressure, with Villa stuck in the relegation zone after a summer of spending.
The club signed 13 new players after beating the drop last season but have not won in the Barclays Premier League since the opening day ahead of Saturday's trip to Chelsea
And Wilkins, who joined as Sherwood's number two in the summer, has warned against firing the manager despite their poor run
"When you're a Premier League manager you're dreading the season's first sacking, because once the first goes the rest seem to buck up a bit of courage and follow suit," he said.
"I think it would be a huge mistake as far as Tim and Aston Villa are concerned.
"He's an up-and-coming manager, he did extremely well at Tottenham and, 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
We'll get there, it's going to be a lot of hard work but we'll get there in the finish."
Villa are four points adrift of the safety line ahead of their game at Stamford Bridge while Chelsea are 16th having won just twice in their opening eight games
Blues boss Jose Mourinho is also under pressure and Wilkins, a former Chelsea player and assistant manager, believes Villa could catch the defending champions cold.
"It's very unusual to see Chelsea in this condition and we're going to go there with a positive mindset and try to get the best result we can," Wilkins told talkSPORT
"We're under no illusions, it's going to be extremely tough for us
"But Chelsea are going through a bit of a difficult time at the moment, so it's a good time for us to meet them."
Source : PA
Source: PA