Suarez, 33, is said to have agreed a deal in principle to join the Italian giants but is not willing to take a pay-cut to join Andrea Pirlo's side.
The news comes in the wake of manager Ronald Koeman stating that Suarez won't be frozen out the first-team should he opt to see out his contract with the Blaugrana.
"Suarez will be one more [member of the squad] if he stays," the Barcelona coach told TV3. "I was talking to Luis this morning.
"We will wait to see if there is a way out or not. We respect contracts and, from day one, we have said that if he stays on the squad, it will be one more."
However, according to Goal, the Uruguayan is seeking healthy compensation to the value of the remainder of his contract if he is to leave on a free transfer to the Bianconeri.