According to Sky Sports News, discussions are ongoing, although sources suggest an agreement is not yet close.
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The 29-year-old has established himself as an important figure under manager Unai Emery, featuring prominently in Villa's campaign.
Buendia has started all seven of the club's Premier League matches this season, contributing one goal.
The Argentina international also found the net in Villa's Champions League victory over Club Brugge and played the entire UEFA Super Cup final defeat against Paris Saint-Germain.