The Argentina international has previously expressed disappointment at the lack of progress, admitting in September that he was "very, very sad" about the situation. However, his father believes there could be movement before the end of the year following changes to Liverpool’s sporting and coaching structures.
"Alexis still has 20 months left on his contract. The sporting director has changed, and so has the manager. The situation is still being assessed, and there could be news before the end of the year," Carlos told ESPN Brazil.
He made clear that there has been no formal negotiation over an extension, although the family would welcome an agreement if Liverpool decide to offer one.
"We haven’t started talks over a renewal yet. If everything goes well, he’ll renew. If not, that’s fine, he’ll go his own way, like so many others."
Carlos also pointed to his son's achievements with Argentina as evidence that the midfielder would have options if his time at Anfield eventually came to an end.
"He’s a young player who has won the Copa América and the World Cup, and finished runner-up at the last one. And he was the Argentine player who ran the most at the World Cup.
"He’s currently the player with the record for unbeaten World Cup matches, 13 games across 2022 and 2026, because he didn’t play the opening match in 2022. Also, he is the player who played the most minutes for Argentina at the last World Cup.
"I mean, he’s got loads of records and achievements, and they’ll help his career continue at top clubs. When you play for Liverpool and want to maintain that same level, you know there are only six or seven teams in the world you can play for."
Despite outlining the possibility of a future elsewhere, Carlos insisted that Liverpool remain the family's sole focus while his son is under contract with the club.
"Right now, we only talk about and focus on Liverpool. That’s the respect the institution deserves and Liverpool fans deserve.
"You can’t be at one club and talk about others. When you’re at a club, you have to give the institution the respect and importance it deserves.
"Today we’re talking about Liverpool, one of the biggest clubs in the world, but whatever the club, you can’t disrespect those who signed you, showed interest in you and made a very significant financial investment.
"We always talk about Liverpool, the passion of representing the club, the dream of winning trophies, and nothing else."
The midfielder's father also believes the uncertainty will not affect his son's performances. He says the priority is to maintain his level on the pitch rather than become distracted by speculation about his next contract.
"He’s in a good place mentally because a player has to understand he only has one great asset: playing well. Every match.
"The only aim is to play well in the next game, and then the next. When you play well, the transfer market and big clubs open up to you. When you play badly, they close. So he has to think about playing well."
Carlos added that the family’s experience in football has helped Alexis navigate the pressures of the profession.
"He comes from a family of footballers. Not just because I was a player, but my brother was too. We’ve had a club for 28 years, my nephew is the sporting director of Deportivo Maldonado in Uruguay.
"I have another nephew who plays in Indonesia, who won the title last year and three million people went out onto the streets.
"We understand football, we know what the profession is like, so we support each other and help each other, and we don’t let anyone lose their way."
A return to Argentina is not being considered, either. Alexis previously played for Argentinos Juniors and Boca Juniors, but his father believes his career remains firmly based in Europe.
"I don’t think any Argentine club today is thinking that Alexis, Enzo Fernández or Julián Álvarez could play in Argentina next year.
"He’s aware that his future is still in Europe. He’s only just turned 27."
For now, Liverpool have time to decide whether to offer the midfielder fresh terms, with his current agreement running until 2028. Carlos has left the door open to an extension, but his comments also make clear that the family will not treat a departure as a crisis if an agreement cannot be reached.