Villas-Boas, who worked under the Portuguese earlier in his career - including a spell at Chelsea when Mourinho was coach there, has endured a tough first season at Stamford Bridge with the Premier League team currently fifth and facing elimination from the Champions League.
The future of Mourinho has also been in the spotlight, despite his success with Real Madrid, with speculation he is set to replace his young compatriot back at the Bridge.
"The only place where Jose's shadow isn't lurking is in Barcelona," Villas-Boas told reporters at the club's training ground in Cobham, south of London, before Saturday's match against West Bromwich Albion.
"His shadow is lurking everywhere else, in the rest of the world, over some of the best managers in the world.
"If you can trade a successful manager for the best manager in the world, well, everybody wants him.
"I think its normal, for the history he left in this football club. The most successful part of this club's history is related to Jose, so its normal."
Last week, Villas-Boas said in an interview with Portugal's TSF radio that he was unsure if he still had the backing of Chelsea's billionaire Russian owner Roman Abramovich while senior player Frank Lampard has said his relationship with the manager was not ideal.
Villas-Boas has left Lampard out of the starting line-up a number of times this season, but said on Friday there was no rift between them.
The 34-year-old maintained their relationship was "good, excellent" adding that they spoke and that "it's just a manager-player relationship in the end."
He added: "Frank's words are genuine. They are genuine from a player that has a reflection of a relationship between us. For me, it's fine, I have no problems with it.
"I have to choose the team and I try to choose the best team for every single game. It hasn't involved Frank a couple of times but it doesn't mean I have a personal problem with him.
"His own interpretation of the relationship is his own but I have no problem with it and I explained it to him.
"They are decisions I have to take for the benefit of the team, always."
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