The Spain international joined the Serie A side in the summer from Atletico Madrid but has found first-team chances hard to come by.
The 28-year-old has been on the bench for the last six Serie A games – sparking rumours he maybe off as soon as January.
Liverpool, according to reports in Italy, are keen on Suarez and may make a move for him in the transfer window.
The player too is open at switching Italy for Anfield and has reportedly instructed his representatives to open negotiations.
La Liga side Sevilla are also interested in the midfielder and could join the race if they receive positive feedback from Suarez.