According to Mail Sport, negotiations have progressed positively in recent days, with both parties nearing an agreement over a two-year extension.
The Argentine's current deal expires at the end of the season, but Villa are determined to secure his long-term future following his impressive resurgence under Unai Emery.
Buendia, 29, has started every Premier League fixture this campaign, establishing himself as an influential figure after previously struggling for opportunities.
The midfielder played a crucial role in Villa's Europa League triumph over Freiburg in Istanbul last May, scoring a spectacular goal.
He also produced another stunning strike in Villa's recent 3-2 victory over Tottenham, continuing his impressive record at Spurs' stadium.