According to Mundo Deportivo, the 35-year-old will be heading off to Argentina, with the Spanish outlet claiming the move could be announced as soon as Monday or Tuesday.
However, the same news outlet claim that River Plate are yet to receive an answer from Suarez whether he will join them.
Despite the reluctance from Suarez, River Plate manager Marcelo Gallardo is relaxed over the situation. He hailed the Uruguayan as an ‘elite player’ who is still showing the ‘will and enthusiasm’ to continue his career.
“There are possibilities,” Gallardo said after River Plate’s 2-1 victory against Lanus on Sunday.
“I think one of the two will clearly happen. But before that, we have to be focused on what we have today.
“If they are signed, it will be to enrich the squad and have another expectation.
“[Suarez] is an elite player, who is currently recovering from a knee injury. We made the attempt. He has the will, and enthusiasm. It’s good.
“If he hadn’t shown enthusiasm, we wouldn’t be here waiting. It will be a decision and when it is possible, we will see if it is feasible. You don’t have to lie to people or generate a lot of enthusiasm.”
Since it was announced that Suarez will not be continuing his stay at the Wanda Metropolitano, several clubs have been courting his services. Serie A side Atalanta were linked to Suarez earlier this month along with Inter Miami.
But it has been revealed that Suarez held talks with River Plate in Paris. The 37-time Argentina Primera Division champions are keen to bring in attacking reinforcements, having lost Julian Alvarez to Manchester City.
Suarez boasts over 500 in his professional career. The Uruguay international has spent two years at Atletico but fell down the pecking order under Diego Simeone in recent months, with the manager preferring Antoine Griezmann, Joao Felix, Angel Correa and Matheus Cunha in the attack.