The wantaway striker, who has made no secret of his desire to quit Anfield for pastures new, could take legal action in a bid to secure a transfer according to John Cross of the Daily Mirror.
Cross claims that Suarez and his agents are considering involving Premier League arbitration in their issue and that the Uruguayan could hand in an official transfer request.
The report also states that the striker's advisers believe they had a gentlemen's agreement with the Liverpool board, which would allow their player to move to a Champions League club if an offer of £35 million was tabled.
Liverpool insist that the only clause met by Arsene Wenger's ambitious bid was one meaning they had to inform Suarez and his management team. Suarez, however, believes he should be entitled to move to the Emirates.
With less than two weeks before the Premier League season gets underway, the Suarez saga is threatening to overshadow Liverpool's otherwise positive preparations for the new campaign.
Wenger appears reluctant to make an improved bid, and it seems as though he believes the actions of Suarez and his agents this week could help him secure a deal for his No. 1 target.
The Frenchman has always been frugal in the transfer market, and it came as a big surprise to see him bid more than double Arsenal's record transfer fee for the ex-Groningen player.
Brendan Rodgers wants at least £50 million if he is to part with arguably his best player, but Arsenal's failure to reach that amount, particularly with almost a month of the transfer window to go, means that this story will run for a while longer.
The Merseysiders have endured a productive window so far, adding Simon Mignolet, Kolo Toure, Iago Aspas and Luis Alberto to their ranks.
What Rodgers and Liverpool cannot risk in the build-up to their season opener at home to Stoke City is letting Suarez disrupt their focus on starting the new campaign well.
With players who are determined to leave, there's a strong argument for negotiating a deal, seeing them on their way and reinvesting the transfer fee on talented, hungry individuals who want to be a part of the club.
Should Liverpool sell Luis Suarez to Arsenal?
While Rodgers' determination to keep Suarez at Anfield is admirable, the last thing the Reds need is for him to end up moving close to—or even on—deadline day.
This would give the former Swansea City boss little or no time to find a replacement, leaving his side noticeably weaker as they head into September's fixtures.
If Suarez does indeed pursue legal action or hand in a transfer request this week, Liverpool may well be better off accepting defeat than continuing to battle a man who doesn't appear to take no for an answer.