Argentine outlet Soy del Millo reports that the 21-year-old has "received an approach" from Villa ahead of the January window, though no details of what that involved, or any proposed fee, have been made public.
It marks a step up from weeks of reports describing only scouting interest, with Villa's and Manchester City's representatives both said to have watched Beltrán in person.
River, for their part, are working to protect their asset. Journalist Renzo Pantich says an agreement to extend Beltrán's contract, which currently runs to December 2027, is "on track," and that the Buenos Aires club want to improve his salary as part of the new deal.
The bigger change would be to his release clause, reportedly rising from around €21 million to as much as €100 million, a sign of how quickly his value has grown.
Beltrán has made 38 appearances for River, keeping 17 clean sheets and conceding 32 goals, and won his only cap for Argentina as a late substitute in a friendly against Honduras in June. He is uncapped at senior level for Italy, for whom he also qualifies.
Manchester City, Atlético Madrid and Real Betis are also credited with interest, though there is nothing new to report on those fronts.
Aston Villa have been building a squad through significant summer spending, including deals for Nicolás Jackson, Johan Manzambi and João Gomes, and a young goalkeeper for the future would fit a recruitment strategy focused on players in their early twenties or younger. Beltrán's own path to the top has been unusual: he arrived at River at 17 with no previous club affiliated to the Argentine federation, having played as an outfield forward in school football before switching to goalkeeper.
The approach puts Villa in a stronger position than their rivals for now, but the timing matters. If River complete the new contract, with its far higher release clause, before any club moves to sign him, the goalkeeper could become a significantly more expensive target than he is today.