Weimann has scored nine goals in 24 appearances this season and has been one of the few positives in a dismal campaign for Villa.
The Austrian international still has 18 months to run on his current deal but Villa hope he will remain as part of the rebuilding process under Lambert.
"For the long term it would be great (if Weimann signs a new contract)," said Lambert.
"I know the club and Andreas are talking at the moment so we'll see what happens there.
"But he has played really well and his goalscoring this season has been excellent. He is without doubt a natural finisher and he's done really, really fine."
Meanwhile, Lambert defended his decision not to consider full-backs Stephen Warnock and Alan Hutton for selection, with the latter poised to complete a loan move to Real Mallorca subject to a medical.
The duo have not played for the first team this season with Warnock having a loan spell at Bolton and Hutton spending time with Nottingham Forest.
Lambert said: "I made the decision. The club needed to be rebuilt in some way. It's a decision I made and it's one I go with.
"It's not being stubborn. I just know the remit of the job. I've got to do what I believe is right."
Mallorca will have the option to agree a permanent deal for Hutton while Lambert also confirmed interest in Warnock from West Ham.