The 21-year-old is said to have rejected the Premier League outfit's recent terms but is willing to continue negotiations.
"It would be great for the long term if Andreas signs," ESPN quotes Lambert as saying. "We're still talking at the minute so we'll see what happens there.
"The way he conducts himself on the pitch and in training is excellent. He has been really on top of his game and taken his chance in the first team."
Weimann has less than 18 months remaining on his current deal.