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The Uruguayan striker is the second top scorer in La Liga -- behind former teammate Lionel Messi -- this season and has scored 19 times in 25 appearances.
Fichajes now reports that Liverpool will 'make an offer' to Atletico in the hopes of bringing Suarez back to Anfield.
Liverpool boss Jurgen Klopp has Roberto Firmino and Diogo Jota as forward options to rotate between, but the Reds are wary over the future of Mohamed Salah.
Salah has been linked with Real Madrid as the 28-year-old Egyptian winger's current Liverpool deal is set to expire in 2023.
According to Fichajes, the potential sale of Salah would 'facilitate the arrival' of Suarez at Liverpool.
Liverpool splashed out £22.7m in 2011 to land Suarez from Ajax as the Uruguayan star made a sensational impact in the Premier League.
Suarez spent three seasons at Anfield and had a phenomenal 2013-14 campaign as he captured the Premier League Golden Boot and PFA Players' Player of the Year award.
The former Barcelona star scored a whopping 82 times and registered 47 assists in 133 appearances at Liverpool.
Suarez left Liverpool in 2014 to complete a stunning £75m move to Barcelona.
Liverpool legend Steven Gerrard admitted that he crossed paths with Suarez and Fernando Torres at the "perfect time" in his glittering career.
The 40-year-old Rangers boss told The Robbie Fowler Podcast: "The reason I always talk about Torres and Suarez is because I felt like I was in my prime at that time.
"I played with you [Robbie Fowler] when I was very young, I was still raw, I was still developing.
"I played with Michael Owen when I was a little bit further along, but I still didn't feel I was in my peak years. I was still getting injury niggles and still finding my feet and my profile.
"I bumped into Torres and Suarez at the perfect time. More Torres because I'm in my peak years in those 2006, '07 and '08 years when I felt like I could go against anyone on the pitch.
"It didn't matter who it was. I felt like I could face anyone at that time. I felt like I was at my peak. They're my best memories from how I felt from a personal point of view."
Featured Image Credit: PA
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