Lampard scored his 150th Premier League goal on Saturday in the Blues' 3-0 win over Bolton but has often struggled to win a first-team berth since the Portuguese manager's arrival.
The midfielder's strike was his 10th league goal of the season, making him the first player to reach double figures in nine consecutive seasons.
And, when asked if he was sure the 33-year-old would be at the club next season, 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."
The former Porto boss was also adamant that he will not be pressured into playing the England international and feels the competition for places in the Chelsea midfield is the reason Lampard is starting fewer games.
He said: "I take no instructions from anybody. 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."
Villas-Boas went on to insist that the Blues must build on their win over the Trotters in order to secure a Champions League place for next year.
He said: "We have not been getting the results and pressure increases on team players and management. You have to deal with that and deliver.
"I just want to go into a run of results, win the next game and build something that we have been missing since the beginning of the season.
"If we get three or four wins in a row, it means a lot because of the knockout ties and that will give us the extra lift and motivation to maybe challenge for another place."