The Uruguay international, who criticised the British press for the treatment he receives in England, has been open about his desire to play for Real Madrid.
"What I always say, the club is the most important thing," The Express quotes Barnes as saying. "If Luiz Suarez doesn't want to be at Liverpool, Liverpool will still survive.
"They've survived from Ian Rush [leaving], people before and people after. I don't have a problem with Luis Suarez at all, but the club is the most important thing."
Recent reports have claimed that Suarez will need to put in a transfer request if he wants to leave Anfield.