They may deny it — but it looks a lot like freshly separated Jennifer Lopez and hunky actor Ralph Fiennes are an item.

The Post caught sexy J-Lo and the suave star of The English Patient embracing in SoHo on Tuesday night. 

They were seen with their arms around each other after dinner at Cipriani on West Broadway. 

"If she [Lopez] was upset by her recent split, she certainly didn't show it," said one eyewitness. 

Last night, spokespersons for Lopez, 31, and Fiennes, 39, offered different answers for their clients' cuddle. 

J-Lo's flack, Alan Nierob, offered a terse "no comment," but Fiennes' mouthpiece, Catherine Olin, insisted that the pair merely had a bite together with a film crew after a day of shooting their new movie, Uptown Girl

"It's utter nonsense. I assume they were just saying goodbye," Olin said. 

Fiennes has been in a long-term relationship with actress Francesca Annis, who is 19 years his senior. She could not be reached for comment last night. 

Both Fiennes and Lopez have failed marriages behind them — he is divorced from former ER star Alex Kingston, and she from hubby No. 1, restaurateur Ojani Hoa. 

The Post's Cindy Adams revealed the bombshell news that J-Lo and new husband Cris Judd were calling it quits after less than nine months of marriage. Yesterday, Page Six reported that she was dating Fiennes. 

While Sean "P. Diddy" Combs' camp has denied a rekindling of J-Lo's stormy romance with him, The Post has learned the rap czar offered her the use of his triplex apartments at 813 Park Ave.

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