The 26-year-old remained at Atletico Madrid after the summer transfer window closed, despite interest from Arsenal and Barcelona, but has struggled to make a decisive impact during the opening weeks of the campaign.
Álvarez has played four matches so far and has one assist, while Jonathan David has started the season strongly and increased the competition for attacking places under Diego Simeone.
The Argentine forward also began the campaign amid frustration from sections of the Atlético support, but the focus has now shifted towards his representation and future.
According to AS, Álvarez is currently without an agent as he looks to replace Hidalgo, whose relationship with Atlético's hierarchy had become increasingly strained.
Gustavo Álvarez has taken control of the process and is looking for a new representative who can offer his son a different direction.
The decision comes only weeks after Álvarez remained at Atlético despite the possibility of leaving during the summer. Barcelona were interested, while Arsenal were also considered a potential destination, although Álvarez did not view a move to the Premier League club as an option.
His immediate future at Atlético is not necessarily in question, however. The season is still at an early stage and there is plenty of time for the forward to improve his performances and establish himself as a key player for Simeone again.
Álvarez's situation is being watched closely because of the uncertainty surrounding his representation rather than because a transfer is currently imminent.
The change of agent could nevertheless become significant if his position at Atlético does not improve over the coming months. A stronger run of form would give the striker an opportunity to quieten concerns about his start to the campaign, while continued struggles could increase speculation over his future.
For now, the priority is finding a new representative. Gustavo Álvarez is leading those discussions, with the family looking for an agent capable of helping determine the next stage of the striker's career.
There is no indication from the available information that Álvarez has decided to leave Atlético. His change of representation is therefore the immediate development, while his performances and relationship with the club will shape what happens next.