Talks between the clubs are ongoing, with only the fee for the striker's services the wrangling point.
Liverpool are holding out for £80m for their star forward - a sum that would activate a release clause in his contract - while Barcelona hope to lure him for a figure in the region of £60m.
FIFA have already confirmed that Suarez will be allowed to have a medical ahead of a transfer, despite receiving a four-month ban from football.
The 27-year-old left the World Cup in disgrace after biting opponent Giorgio Chiellini during Uruguay's group defeat to Italy.
But an eventual apology for his latest indiscretion has smoothed the way for a switch to Spain and Barcelona's sporting director, Andoni Zubizarreta, publicly backed the striker earlier this week.
"Suarez had the honour to come out and apologise for his actions and now it's time for him to begin the recovery process," Zubizarreta said.
On Wednesday evening a Liverpool source confirmed: “The talks held today were productive, there are sensible expectations on both sides. Further talks and discussions are to take place, but nothing is finalised as of now."