Tottenham are locked in a race for a Champions League spot with the Blues and Arsenal, and the 35-year-old is sure the newly crowned champions will not take their foot off the gas
The third-placed Blues are in pole position for Champions League qualification, sitting one point ahead of Arsenal and three ahead of Spurs.
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"Players who win titles have a great winning mentality and want to win every single game," Villas-Boas told reporters. "So I expect Chelsea to have a very, very difficult game and Manchester United to be at the top of theirs.
"Sir Alex is an extremely competitive manager so I have no doubts about what he does. We saw an example of that against Arsenal and I don’t think Manchester United will be doing anything differently against Chelsea, particularly after being knocked out of the FA Cup by them."
Elsewhere, Arsenal face already-relegated QPR, whilst Spurs take on Southampton, and Villas-Boas believes the Rs will be keen to bow out on a high.
He added: "Harry [Redknapp] wants to continue to compete. QPR players will probably play without pressure and you never know that may help them.
"All the fixtures are pivotal. We have to do our job first and see what happens on Sunday. The vital thing is to win against Southampton and then face Chelsea with that extra motivation."