The Guardian says Barcelona have made the eye-watering offer after a club source revealed "productive talks" have been held between the two clubs.
A Liverpool source told the Guardian: “The talks were productive. There were sensible expectations on both sides and there will be further discussions to take place. But nothing is finalised as of now.”
Furthermore, according to Catalan radio station RAC1, talks for the Uruguay striker have reached a "crucial stage", with the Spanish club sending their chief transfer negotiator Raul Sanllehi for discussions with the Liverpool hierarchy on Wednesday.
However, in Spain the value of the bid has been put nearer £56 million.
The Daily Mail is even reporting that the fee offered by Barcelona could be as high as £72m.
The fee is short of the £80m Liverpool were apparently set to demand, but it would still be a club record, eclipsing the £50m they received for Fernando Torres.
Suarez will of course be banned from the initial stages of the coming season after the four-month ban handed down by FIFA after the Uruguayan bit Italian defender Giorgio Chiellini in their group game at the World Cup.
With Sanchez apparently out of the picture, it seems unlikely that Liverpool would accept a lower cash figure than they were looking for, so although negotiations are clearly underway, this saga could have some time to run yet.
WHAT BARCELONA SAID
Barcelona president Josep Maria Bartomeu refused to confirm the club were in talks with Liverpool, but did praise Suarez over his apology for the Chiellini incident.
"I announced months ago that the team would undergo a deep renovation but we cannot reveal details because we don't want to give clues away to any of our rivals," Bartomeu said on Wednesday, as they confirmed the signing of Sevilla midfielder Ivan Rakitic.
"Our representatives are constantly travelling to other countries because of potential signings.
"Suarez is a Liverpool player so I can't talk about him, he belongs to another team, a rival team. But we are all football men, and saying sorry is honourable, it helps the competition.
"He did something that wasn't right, so it's the responsibility of everyone in football, be it Liverpool or anywhere else, to remember that he has said sorry. Admitting you have done something wrong is very important.
"Luis has apologised and that is honourable, he's taken a step towards rehabilitating, the football world should support him and help him," added Bartomeu. "As a football fan I hope he can turn a corner."
It's an open secret that the two clubs have held a meeting over what could well be the blockbuster deal of the summer, but whether these latest reports are absolutely accurate remains to be seen. The Spanish media - and English for that matter - can be prone to misinformation but it would make sense for Barca to test the water and the fact that stories are emerging from both countries suggests they could be true. Barcelona might have to up their offer somewhat, though.
- Sports & Recreation