Arsenal want to move on the Portuguese left-back this summer following the arrival of Oleksandr Zinchenko from Manchester City last week.
The Gunners are focusing on offloading several players in the coming weeks and Tavares is one of the top names on that list.
Atalanta have been in talks with Arsenal to sign the 22-year-old on loan and there were claims that the two clubs are close to agreeing on a deal.
However, the negotiations are not as advanced and, according to Italian broadcaster Sportitalia, the deal might not happen at all.
Atalanta have cooled their interest in the player and could be looking at alternative targets.
Tavares has been keen on the move but it seems Atalanta are unlikely to try and sign him this summer.
Brighton have also been linked with an interest in the player, but the Seagulls have dismissed the speculation.
Arsenal are keen to find a new club for Tavares as he is not part of Mikel Arteta’s plans going forward.