The 26-year-old Polish keeper has been linked with Celtic.
Levein said: "Lukasz has been playing really well and, because of that, we've made him an offer of a new contract which he and his agent are thinking about right now.
"We'll find out if he wants to stay or not. If he doesn't then so be it, that's the way the game works.
"I've told him that the best thing for him is to stay here for a while yet because he's been playing regular and is improving."