The Argentina international remains in firm focus over a possible exit after his belated return to preseason training after reaching the 2026 FIFA World Cup final in July.
Alvarez shocked the club during the tournament as he openly confirmed his desire to leave Madrid to join Barcelona this summer.
That stance has not changed from Alvarez's perspective, despite head coach Diego Simeone and club CEO Miguel Angel Gil Marin confirming their intention to block any offers, and reintegrate the striker back into Atleti's squad.
He is yet to feature for Simeone so far this season, amid rumours he may refuse to train in the coming weeks, to try and force an exit.
Real Madrid saw a reported bid rejected last month - with Barça also thwarted - as both offers came way below Atleti's valuation of the former Manchester City attacker.
Arsenal are also rumoured to be tracking the situation with interest, but sources in Spain claim Alvarez will not accept a move back to England, and he only wants Barcelona - if Atleti relent on their current position.