Lampard has admitted that there are "certain issues" between himself and the manager, and Villas-Boas has defended his team selection which has often seen the England midfielder benched.
The 33-year-old has still started 19 Premier League games this season, and on Saturday became the first player to reach double figures for goals in the Premier League in nine consecutive seasons.
Asked if Lampard will remain at Stamford Bridge, Villas-Boas said: "I hope so. 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."