The veteran midfielder admitted this week that his relationship with the Portuguese coach has not been ideal, amid rumours that he may leave the Stamford Bridge outfit in the summer.
Despite this, Lampard started the game against Bolton on Saturday, and scored a goal in the 3-0 win.
Villas Boas wants to keep the England international in West London, and was full of praise for him after the game.
“I hope so,” the tactician told reporters when asked if Lampard would stay.
“It does not depend on me. It depends on three parts – I want him, the person wants to stay and the club wants him.
“Frank goes on and on breaking the club’s records and that is important for him. I congratulate him for that.
“He is a player who has been involved with all managers before and played in most of the games.
“The only difference this year from the years before is that we have more competition in midfield and things become more difficult for everybody.
“But Frank is now in the top five of players most used so he is up there with the best,” he concluded.
By Gareth McKnight