DiCaprio, 37, has told Pattinson, 26, that if he needs a night out, he will be happy to host a party. The two have been put in touch through their mutual friend, actress Reese Witherspoon.
"Leo has been one of Rob's role models for years, and Rob was totally taken by surprise when Leo called him," contactmusic.com quoted a source as saying.
"Leo invited Rob along on a getaway he's planning when he's in Puerto Rico for the wrap party on the movie he's producing, 'Runner, Runner'," the source added.
Pattinson broke up with Stewart after the news of her affair with her "Snow White And The Huntsman" director Rupert Sanders surfaced.