The news could explain the 2008 world champion's uncharacteristically bad mood last weekend in Korea, where he vowed to begin to "redeem" himself after the worst period in terms of form and incidents in his career.
The Daily Mail says 26-year-old Hamilton's split after four years with American pop singer Nicole Scherzinger, 33, is because of their "conflicting work schedules".
Separate spokesmen for Hamilton and Scherzinger did not comment.
But the news was also reported by the Daily Mirror and the Sun, with a source saying the pair have "agreed there's no point as they never see each other".
10/17/11 (GMM) Second place improved Lewis Hamilton's mood in Korea, but not much.
The unshaved 2008 world champion was strangely miserable as he started from pole in Sunday's grand prix, but he at least managed some small smiles after finishing the race behind Sebastian Vettel.
His mood, however, had triggered some wild speculation, including that he has split with his girlfriend, joined the celebrity religion Scientology, or had a raging row with his McLaren bosses.
On the latter theory, Hamilton told reporters: "Whoever wrote that, it's a load of rubbish; I am very happy."
But he also admitted that a single second place was not going to completely brighten his misery after what he calls the "worst year" of his career.
"So if you expect me to be all happy-doolally after a race like that you're not going to hear it," said the 26-year-old.
On Monday, the British Mirror and Daily Mail tabloids are reporting that Hamilton is on the verge of splitting with his Pussycat Dolls girlfriend Nicole Scherzinger.
But the British driver on Sunday indicated that it is the specialist motoring publications that worry him the most.
"Time will tell," Hamilton said when asked if his performance had "redeemed" him after a run of bad races.
"It depends what you guys write. It depends how people perceive how the race went, how my attitude is, how I behaved. I am sure it is a few brownie points that I scored.
"It's (about) positivity, positive stories, positive fans, it's standing on the podium smiling. It's that energy that you get that stays with you until the next race and then you do it again," he added.
|Lewis Hamilton and his girlfriend|
10/16/11 (GMM) The rumors are swirling after Lewis Hamilton's troubled 2011 season took another twist in Korea.
The 2008 world champion, recently locked in a dispute with Felipe Massa after a spate of incidents, did not return a radio message on Saturday after his engineer applauded his pole position.
"It is not obligatory to whoop," said McLaren team boss Martin Whitmarsh.
But there is more to it than that. Hamilton, 26, did not wave after emerging from his cockpit in parc ferme, try to avoid a cameraman with his shoulder, smile once during the press conference, or raise his voice above a monotone.
The interviewer's first question to the unshaved Briton was: "Is everything ok?"
His quiet answers did nothing to prevent the ensuing rumors.
The Independent's David Tremayne believes Hamilton had a raging row with his McLaren bosses after Suzuka, where his on-form teammate Jenson Button won.
"There is talk among McLaren insiders of words being said in the aftermath of Suzuka that cannot be taken back", he reported.
Correspondents for the Corriere dello Sport and O Estado de S.Paulo newspapers, meanwhile, claim Hamilton's mood might be explained by his apparent joining of the controversial celebrity religion Scientology.
A tamer theory is that he is struggling to accept Jenson Button's ascension to prominence at McLaren, a team he has been contracted to since childhood.
"I don't think that relationship (with the team) has been affected by Jenson," Hamilton is quoted by the Express newspaper.
Virgin team boss John Booth, who knows Hamilton well after running him in formulas Renault and F3, thinks the explanation is simpler still.
"My guess is this is just a little bit of pressure and he will relieve it with a win and he will be off again," he said.
"It is like a striker having a non-scoring spell. It weighs on them heavily and then suddenly they score and keep on scoring. Lewis is one of the very best drivers out there."