The Argentina international, having recovered from an ACL injury suffered last season, is now inside the final 12 months of his Villa contract.
DSports says River have now made contact with Villa about the prospect of ferrying Buendia away.
For his part, Buendia was happy to stay in August as loan offers arrived.
However, the midfielder comes from a family of River fans, as he has admitted in the past: I’m from River (fan of River Plate), a family of River since I was young.
"I like to follow them, I try to follow Argentine football even though it costs because of the time difference.
"I always dreamed of playing with a ball, playing with River. I never closed the door but today, my head is in Europe. Tomorrow, we will see. I would like it because it’s the club I support but we will see in the future."