Villa and Arsenal were both reported to have made offers of £30m for Buendia in recent days.
The Argentina international played a huge role in helping Norwich return to the Premier League at the first time of asking.
The attacking midfielder scored 15 goals and registered 16 assists in 39 Championship appearances last season.
Arsenal are in the market for a creative player following Martin Odegaard’s return to Real Madrid after his loan spell at the Emirates.
But it will not be Buendia who will be joining Mikel Arteta’s squad.
The Athletic say Villa are expected to announce the signing of Buendia on Sunday.
It will be a club-record sale, with the deal rising to £35m.
The highest previous fee Norwich have received for a player was the £25m they sold Ben Godfrey to Everton for last year.
Buendia underwent his medical on Saturday in Argentina ahead of his country’s participation in the Copa America.
MORE TO FOLLOW
For the latest news and breaking news visit: express.co.uk/sport/football
Stay up to date with all the big headlines, pictures, analysis, opinion and video on the stories that matter to you.
Follow us on Twitter @DExpress_Sport – the official Daily Express & Express.co.uk Twitter account – providing real news in real time.
We’re also on Facebook @DailyExpressSport – offering your must-see news, features, videos and pictures throughout the day to like, comment and share from the Daily Express, Sunday Express and Express.co.uk.