It is only two years ago that Atletico paid Villarreal around £17m to land the striker, but it has not gone well since.
Vietto has managed just 12 LaLiga starts for the club and was shipped out on loan to Sevilla last term.
He scored six times in 21 league games during what was considered a mixed spell for the Argentinean.
And now, despite Atletico being under a transfer ban, they are looking to move him on again before the window closes.
According to Spanish newspaper Sport, they are hoping to sell him permanently and recoup some of the money they spent on him in 2015.