The paper also quoted a Uruguayan journalist who tweeted that Suarez had told him he was staying at Anfield.
"Luis Suarez confirmed to me he won't leave Liverpool. The support of the fans in recent weeks influenced the decision," journalist Martin Charquero wrote on his feed.
He added that Suarez would seek "a probable renewal of the contract that ties him to Liverpool".
Last weekend, Liverpool manager Brendan Rodgers told Suarez that he must apologise to the club and supporters if he wanted to mend relations with them and be welcomed back into the squad.
Rodgers has made Suarez train alone after the Uruguayan sought a move away from Anfield on the grounds that they had failed to qualify for the Champions League.
Liverpool turned down a 40 million and one pound ($62 million) offer from Premier League rivals Arsenal after Suarez said he wanted an "amicable agreement" to leave Anfield, thinking any bid over 40 million would trigger a release clause in his contract.
Suarez, who scored 29 goals in all competitions last season, has received full backing from the club and the solidarity of supporters despite two controversial incidents that have marred his two-and-a-half years on Merseyside - the racial abuse of Patrice Evra and biting Branislav Ivanovic's arm.
Liverpool and England captain Steven Gerrard said he was determined to do all he could to keep Suarez at Anfield.
"It's very important he stays. He is one of the best players in the world," said Gerrard, who will lead England against Scotland in a friendly at Wembley later on Wednesday.
"I can understand why clubs are showing an interest in him (but) 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," he was quoted as saying by the Daily Mail.
(Additional reporting by Felipe Llambias; Writing by Rex Gowar in London; Editing by John O'Brien)
