Speaking in Tokyo ahead of Uruguay's friendly with Japan, Suarez appears to have backtracked on his desire to leave Brendan Rodgers' side.
The report includes a quote from Suarez which appeared in Uruguayan newspaper El Observador. The former Ajax forward is simply quoted as saying: "For now, due to all of the people's affection (for me), I will be staying."
If true, Suarez appears to be referring to the support he received from Liverpool fans during Steven Gerrard's testimonial match at home to Olympiakos and during the club's preseason tour.
The Daily Mirror report also makes reference to some tweets late on Tuesday evening by respected South American journalist Martin Charquero, who claims that Suarez may even sign a new deal with the Merseyside club.
Charquero tweeted (as quoted in the Mirror):
Luis Suarez confirms to me he will not leave Liverpool. The support of the fans has influenced his decision.
Suarez see (sic) it as likely that he'll sign a renewal (extension) to the contract that binds him to Liverpool.
Suarez had been caught in a long-running transfer saga after announcing his wish to join a new club this summer.
In an interview with The Guardian, Suarez claimed that the club would allow him to leave if they failed to reach the Champions League. He said:
I don't feel betrayed (by Liverpool) but the club promised me something a year ago just as I promised them that I would stay and try everything possible to get us into the Champions League.
They gave me their word a year ago and now I want them to honour that.
However, Liverpool dismissed this was the case, as per an ESPN FC report, and have stood firm in their refusal to allow Suarez to leave.