According to Globo Esporte, Viveros had been close to agreeing a new deal with the Brazilian club before negotiations reached a deadlock.
The 26-year-old striker is currently contracted until 2027, with an option for a further 12 months, but his performances have attracted growing attention after a prolific season in Brazil.
Viveros has scored 18 goals in 26 league appearances and recently made his Colombia debut in a 1-1 draw with Mexico.
His international breakthrough has added to the interest surrounding his future, with Globo Esporte reporting that the striker has also signed with agents CAA Stellar Sports amid expectations that he could leave Athletico at the end of the year.
The report puts a potential transfer fee at around €20m.
Aston Villa have previously been linked with Viveros, with the Premier League club's interest dating back to the summer.
Sunderland are also reported to have sought information about the striker as clubs assess his availability.
Viveros' situation has changed since those initial links, with the stalled contract negotiations potentially increasing the possibility of a move when the transfer window reopens.
The forward has taken a long route to the top level of South American football, having played in Colombia, Venezuela and Bosnia & Herzegovina before establishing himself in Brazil.
His 18-goal league return has made him Athletico's leading scorer and placed him among the more closely watched forwards in the Brazilian top flight.
The Colombia call-up represents another significant step in his development.
Globo Esporte reports that Viveros had been expected to agree fresh terms with Athletico before the negotiations stalled.
His existing contract gives the Brazilian club some protection, with a further year available through the extension in his current agreement, but the reported €20m valuation could now become relevant if interest from Europe develops into a concrete offer.
Villa have since strengthened their attacking options with the signing of Nicolas Jackson, who is expected to provide competition and support for Ollie Watkins.
The club also has young forward Brian Madjo, who impressed during pre-season.
Viveros would therefore represent another attacking option rather than simply a direct replacement for an existing player.
The immediate focus is now on the striker's future at Athletico following his first Colombia appearance and the breakdown in talks over a new contract.
With Villa and Sunderland among the clubs reported to have gathered information, his performances during the remainder of the year are likely to remain closely watched.