Alvarez told the club during the 2026 FIFA World Cup that he wanted to leave Madrid and join LaLiga rivals Barcelona.
Atleti consistently maintained their position over not wanting selling Alvarez to the defending Spanish champions after a furious war of words between the two clubs and he remains in place in the Spanish capital.
As the saga rolled on, Atleti dug in and refused to engage over a sale, with Barca informed there was '0% chance' of a deal.
The Los Rojiblancos faithful have reacted negatively to Alvarez in the aftermath and booed him on several occasions so far this season.
Diego Simeone has confirmed his intention is to utilise his fellow Argentinian this season, but Godin believes it could be difficult to find a way back with the fans.
"It's a very complicated situation, as it's been like all summer, it's not easy to handle. Seeing him declare he wants to leave isn't easy.
"For a fan, it's like a stab in the back. Hearing your best player say he wants to leave is never pleasant.
"I empathise with Koke, the other players, and Simeone, who have to go to press conferences to defend and protect him because he's young.
"I don't think he's a bad person, he simply has the desire to go. The club took a risk by keeping him, now we have to make sure he feels good, and performs well on the pitch; that's what the fans expect."