Weimann still has 17 months to run of his current three-year contract believed to be worth around £15,000 a week.
Villa hope the Austrian international will commit himself to a long-term future with the Midlands club.
They view the opening negotiations with his representative as positive.
Villa sources insist that talks will be ongoing to try to tie up the services of a player who has scored 10 times in his first full season of senior football.
The Austrian Under-21 international joined Villa from Rapid Vienna five years ago.
Villa manager Paul Lambert has described Weimann as "a natural finisher" and he has been one of their best performers during the battle for Barclays Premier League survival.
Weimann has slotted in effectively alongside 15-goal Christian Benteke - often at the expense at club record signing Darren Bent.
Lambert recently said: "It would be great for the long term if Andreas signs (a new contract). The talks have been ongoing."