“They’re not ready for that, at least as far as Jake.” The pair first met on the Morocco set of the movie Rendition in 2006.“Jake went and introduced himself to Reese,” a source close to both told PEOPLE.

goes on to make it sound like Reese and Jake have broken up several times, the working (and unspoken) theory being that Reese and Jake did actually break up a few weeks ago, but might get back together yet again. While the precise status of the Reese Witherspoon and Jake Gyllenhaal relationship remains unclear – over the weekend a source close to the actress told PEOPLE the couple had split, a claim denied by their reps – the two have certainly had their share of highs and lows during their two-year relationship.

Another claim: Jake wants to marry Reese (“Jake would marry her tomorrow”) but Reese is gun-shy about re-marriage and strictly adheres to a “if it ain’t broke, don’t fix it” philosophy (“Jake can be a little overbearing at times, and Reese is really happy with life right now. Witherspoon, 33, told close friends around Thanksgiving that she and Gyllenhall, also 33, had broken up, says the source.

A new report claims the genetically gifted duo were recently seen parading around their affection for one another in NYC during multiple dates.

The actor and 35-year-old actress dined at Lugo Caffe last Saturday, June 7, before heading off to Madison Square Garden to catch the boxing match between Miguel Cotto and Sergio Martinez. They were in deep conversation," an onlooker at the eatery says.

Brooks) and in Pittsburgh (where Jake is shooting his new movie, Love and Other Drugs).

“As much as everyone thinks they’re right there, they’re really not near the whole marriage thing,” a source close to the couple told PEOPLE last spring.

" Unfortunately, the 31-year-old would not reveal the name of the partner who joined her for the late night rendezvous.

It was reported Reese and Jake joined the Mile High Club on a flight from Germany to LA in 2007.

Eventually, the actress would head to the bathroom — with Jake trailing closely behind.

“I started timing them — they were together in there for 11 minutes,” the eyewitness shared.

Like Rachel, Jake has also dated a bevy of beauties.