The 29-year-old is out of contract with the Scottish Premiership champions at the end of next season.
The right-back has one year left on his current deal with the Hoops. And he confirmed that the ball is completely in the club's court regarding a new contract.
"Next season is the last year of my contract. Of course it's up to Celtic as well what happens," he told the Daily Record.
"I'm just focusing on playing for the club over the next year and we'll see what happens. Last time I signed a new contract it was Celtic who came to me, so at the moment I'm just sitting quietly in my boat."
Given Lustig's contribution this season, Ronny Deila may want to ensure that he is tied down long before his contract reaches its final months to prevent any speculation regarding his future. The 29-year-old has made 39 appearances in all competitions for the Bhoys this term, and has played more games in the league than in any other previous campaign since joining them in 2012.
However, the club may also be wary about offering too long a deal to a player who will be 30 by the time it commences. The performances of Kieran Tierney on the other side of defence this season have proved that there are youngsters capable of earning a first-team spot in positions where there are experienced members of the squad already present.
And given his previous injury record, the champions may want further proof that his past problems are behind him before they offer him fresh terms.