The Premier League side were keen on the 24-year-old, who spent time earlier in his career with Newcastle, but owner Gino Pozzo confirmed the deal was dead on Thursday morning.
Santon, a youth product of Inter, returned to the Italian club in January on loan from Newcastle and made nine league appearances for the Nerazzurri.
Inter made Santon’s move a permanent one last month once the player’s contract with the Magpies had expired.
“I can say that the deal is now off the table and negotiations will not continue,” Pozzo said.
“I see no particular enthusiasm in the lad, despite all the time that we gave him to reflect and evaluate the deal.
“At this point it doesn’t seem logical to put pressure on the player. It’s a pity because we had an agreement on everything but Santon doesn’t want to leave Inter.”
Pozzo did confirm an interest in another Inter player, French midfielder Saphir Taider, who spent last season on loan with another Serie A side Sassuolo.
“Right now we cannot talk about a proper negotiation,” Pozzo added. “For the time being it’s a possibility that we are all evaluating. We do like the player.”