Is there a bromance brewing between Leonardo DiCaprio and Robert Pattinson? That's what some sources are claiming, after DiCaprio reportedly invited Pattinson to join him for a private party he is planning in Puerto Rico, to celebrate the wrap of "Runner, Runner," a film he is producing.

"Leo wants to book a mansion at a secret location on the coast so he and his pals can party in private. He's kept an eye on Rob's career ever since people started calling him the next Leonardo DiCaprio. Leo figured it would be great for him to hang out with a bunch of laid-back guys," said a source for Showbiz Spy. "Leo joked they could compare baseball cap collections - and told Rob before he knew it, he'd be dating a model, just like him!" (DiCaprio is currently dating 23-year-old lingerie model Erin Heatherton.)

DiCaprio and Pattinson were allegedly introduced by mutual friend Reese Witherspoon, who worked with Pattinson on the 2011 film "Water For Elephants," and whose home Pattinson famously stayed in after news broke of his girlfriend Kristen Stewart's affair with Rupert Sanders. Witherspoon and DiCaprio met 2 years ago at a fundraiser for Haiti.

Pattinson has weathered a storm of very public media humiliation and speculation about his personal life in the weeks that have elapsed since the Stewart-Sanders scandal. Pattinson recently sold the Los Feliz home he shared with Stewart, and on Monday, Creation Entertainment, the company behind the "Twilight" conventions, released a statement informing fans that neither Stewart nor Pattinson would be appearing at the fan conventions to celebrate the last film installment of the "Twilight" series, "Breaking Dawn - Part 2."

"The passion and dedication of Twilight fandom has been amazing and we're out to throw one last giant convention, a final gathering to see old friends that have made up the Twilight family," the company said, in an official statement.

"Although Rob, Kristen and Taylor will not be with us this time out we will have a super line-up of other Twilight stars and the weekend will be filled with special events, movie prop and costume displays, contests, panels, auctions, parties, exclusive merchandise, music and much more, including some surprises!"

But while Pattinson has been seen partying, doing promotional events for his film "Cosmopolis,"and generally continuing on with his life, Stewart has kept out of the public eye. Stewart hasn't committed to any public appearances until Sept. 6, when she is scheduled to promote her new film "On The Road," an adaptation of the Jack Kerouac novel, at the Toronto Film Festival.