That’s according to Spanish daily Sport who say the Catalans have offered Liverpool a significant sum of cash plus a player.
The Reds are demanding top whack to part with their prized asset and Barce are keen to try and drive the figure down.
Turan and Suarez are both peripheral figures at the Nou Camp.
Turkey international Turan, 30, played just 18 La Liga games last term and is deemed surplus to requirements.
Suarez, 23, is highly-rated but he managed only 12 starts last season and could also be moved on.
Rafinha was an ever present in the Barca first-team last season.
However, he was deployed primarily at right-back and Nelson Semedo has just been drafted in from Benfica.
Barca will have cash to splash once Neymar completes his mega-money move to Paris St-Germain.
The French giants are expected to cough up a staggering £199m for the Brazilian superstar.
Coutinho, 25, scored 14 goals and provided nine assists for Liverpool last season.