Villas-Boas joined the Stamford Bridge outfit during the summer after his success at Porto last season, in which he won the treble.
But his reign has not been as successful as he would have expected, with the West London club currently fifth in the Premier League and dangerously close to exiting the Champions League at the group phase.
Following unexpected 2-1 defeats against Liverpool and Bayer Leverkusen respectively, reports have suggested that Villas-Boas' short time in England could soon come to an abrupt end if results do not improve quickly.
However, Wilkins, who was also assistant manager at Stamford Bridge before his controversial departure in 2010, believes the Blues are suffering a transitional period and must stick by their manager.
“Chelsea have a very high quality of player at the club, and once they kick in I can see no reason why they will not put in a very good showing,” he told Yahoo!
“It's a transitional period, and Villas-Boas will have his own ideas about where he wants the club to go, and regarding specific personnel.
“It is a transitional phase, so Chelsea must give him time.”
Although the 55-year-old is a fan of Villas-Boas, Wilkins did state that the Portuguese's choice of tactics may one of the reasons behind Chelsea’s on-pitch struggles, and is unsure whether the tactician has made progress during his tenure.
“It is very difficult to say whether there has been progress under Villas-Boas, because it has been tough times,” he added.
“There has been a few players brought in, and the system has changed quite a lot.
“AVB wants his players to press higher up the pitch, and that can consequently leave space in behind.
“They are finding it very difficult to keep clean sheets at the moment which is very unfortunate, but I think they will be OK.”
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By Matt Maltby
