Weimann has been one of the few plus points in a dismal season to date for Villa and he is their second top scorer with nine goals behind Christian Benteke.
The Austrian international still has 18 months to run on the deal he signed in August 2011 but Villa hope he will remain as part of the rebuilding process under Lambert.
Lambert said: "For the long term it would be great (if Weimann signs a new contract).
"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."
Lambert has defended his decision not to consider full-backs Stephen Warnock and Alan Hutton with the latter set to complete a loan move to Real Mallorca on Tuesday subject to a medical.