The 21-year-old has been one of the only positives from a dismal season for Villa, scoring nine goals in 24 appearances this term.
The Austria international has 18 months remaining on his current deal, and Lambert is keen to see the forward commit his long-term future to the club.
“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 to drop out-of-favour duo Stephen Warnock and Alan Hutton despite their unquestioned top-flight experience.
Hutton and Warnock are yet to make an appearance for the Birmingham outfit this season, with the former Rangers full-back on the brink of joining La Liga’s Real Mallorca.
“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,” said Lambert.
“It’s not being stubborn. I just know the remit of the job. I’ve got to do what I believe is right.”