Suarez had been determined to leave the Anfield club, but according to a Uruguayan journalist the loyalty of the Liverpool fans has won him round.
Arsenal have had two bids rejected for the controversial forward, and had plans for a third offer approaching Liverpool's minimum £50million asking price.
Lean on me: Luis Suarez claims he wants to stay at Liverpool, according to Uruguayan media
Lean on me: Suarez claims the loyalty of the Liverpool fans has won him over as the club battle to keep him
In action: Suarez got a huge response from Anfield when appearing in Steven Gerrard's testimonial
THE SAGA OF THE SUMMER
June 17 Suarez says he wants to leave Liverpool while on duty with UruguayJuly 8 Suarez admits he is flattered by interst from Arsenal
July 17 Suarez's agent tells clubs to bid £40million to test a clause in the striker's contract
July 24 Arsenal bid £40million plus £1 for Suarez in the belief it would trigger a release clause
July 24 Liverpool owner John H Henry tweets 'What do you think they're smoking over there at Emirates?'
July 30 Liverpool boss Brendan Rodgers says Liverpool haven't had any bids for Suarez matching their valuation.
August 4 Suarez appears in Steven Gerrard's testimonial
August 6 Suarez left out of Liverpool's pre-season trip to Norway with foot injury
August 7 Suarez blasts Liverpool over breach of contract, demanding they let him leave
August 10 Rodgers insists Suarez is not for sale
August 11 Rodgers says Suarez must apologise before he is welcomed back
August 12 Suarez refuses to say sorry, still believing the club have betrayed him.
August 12 Rodgers says the relationshp between Suarez and the club can be resolved.
August 14 Uruguayan media claim Suarez now wants to stay at Anfield
But Suarez - now on international duty in Tokyo - may now stay at Anfield.
'For now, due to all of the people's affection (for me), I will be staying,' he told Uruguayan newspaper El Observador.
Uruguayan journalist Martin Chaquero also claimed he had been told Liverpool will keep their star man.
'Luis Suarez confirms to me he will not leave Liverpool. The support of the fans has influenced his decision,' Chaquero said.
'Suarez see it as likely that he'll sign a renewal (extension) to the contract that binds him to Liverpool.'
Although Suarez may be indicating he is ready to sign a new contract at Anfield, Sportsmail understands that is a long way from happening due to his behavior over the last month,
The news comes after Reds captain Steven Gerrard admitted he will use his influence at the club to try to persuade the striker to stay.
‘It’s very important he stays. He is one of the best players in the world,’ Gerrard said ahead of England’s Wembley friendly against Scotland. 'I can understand why clubs are showing an interest in him.
‘If I can use my influence to make him stay I will. I love playing with him and I don’t want him to go.’
'For Liverpool to be successful and move forward we have to keep our best players. I don't know what will happen in the next two weeks,' Gerrard said. 'But I'm really confident he won't move to anyone else in England.'
Meanwhile, Arsenal are devising a Plan B in their search for a new centre forward as the realisation dawns that they could miss out on Suarez.
Sportsmail understands the Gunners’ back room team have started looking at a contingency plan should their pursuit of Suarez end in failure.
Bid: Steven Gerrard (right), training with England, says he will try to make Suarez stay at the club
Interested? Edin Dzeko, pictured in Munich with Manchester City, has found form in pre-season
Other targets: Stevan Jovetic (right) chose Manchester City but Michu (left) remains an option for Arsenal
One that got away: Gonzalo Higuain (centre) left for Napoli. Here, he celebrates scoring against BenficaDiscussions aimed at identifying alternative targets between scouting staff have taken place in the last few days.
The news is the first clear indication from within the Gunners ranks that they could miss out on Suarez, who has become the major focus of their transfer strategy.
Gonzalo Higuain and Stevan Jovetic both featured highly on Arsene Wenger’s wanted list this summer, with a deal for the former virtually completed before the Gunners switched their attentions to Suarez.
But the strike pair have already completed big-money transfers this summer, Higuain to Napoli and Jovetic to Manchester City, leaving the Gunners short of options.
Wayne Rooney was a target earlier in the summer, while the club have completed extensive scouting reports on Swansea striker Michu and Manchester City’s Edin Dzeko.
Liverpool insist they will not sell Suarez to Arsenal under any circumstances, but the Gunners are not giving up on trying to land the Uruguayan - who is desperate to quit Anfield for the Emirates.
One player Arsenal look better placed to sign is Bayern Munich defensive midfielder Luis Gustavo.
The Gunners have opened talks with the Champions League holders over a £14.5million switch for the Brazil international.
Still searching: Arsene Wenger (right), talking to Manuel Pellegrini, is looking to add to his squadAnd Gustavo, who has dropped down the midfield pecking order at the Allianz Arena, is keen on a move to north London, saying: ‘They [Arsenal] are a great team and that would be a great chance.
‘I want to move to a club where I can play.’ Meanwhile, Malaga want to use right-back Jesus Gamez as part of the negotiations to sign Nicklas Bendtner.
Arsenal want to sign a new right-back as defensive cover for Bacary Sagna, who could be used as a makeshift centre back in the absence of injured Thomas Vermaelen during the opening weeks of the season.
And Malaga want to explore using Gamez, 28, as part of the deal to land Gunners outcast Bendtner.
Ins and outs: Luiz Gustavo (left) could join from Bayern Munich whereas Nicklas Bendtner is likely to leave
