Arsenal want the 22-year-old Argentine, according to reports.
The out-of-favour striker scored three times in 15 starts for last season's Champions League finalists in a run of form which has prompted speculation over his future.
He joined Atletico from Villarreal for £15 million last summer and talkSPORT claim that the Madrid club would let the 22-year-old leave if they recouped that fee.
Vietto - who was linked with a move to Arsenal last summer but joined Atleti because of fellow Argentine Diego Simeone's presence according to The Express - may not be against the idea of leaving.
The youngster netted 18 goals in 28 starts for Villarreal during the 2014-15 campaign, according to ESPN, and he will want enough playing time to help him scale those heights once more.
And the Gunners could do with another striker.
Aside from Olivier Giroud, the North Londoners don't really have an out-and-out centre-forward, which arguably cost them Premier League glory last term when the Frenchman went 15 league games without finding the net.
Arsene Wenger can ill afford to make a similar mistake in what could be the final year of his 20-year spell at Arsenal. Wenger, whose last title came back in 2004, will be desperate to put things right next term.