The Austria 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."