Blake Lively and Ryan Reynolds heat up off-screen, reportedly visit one another on film sets 
 
 Eric Charbonneau/WireImage Blake Lively and Ryan Reynolds are reportedly the latest hot item on the red carpet. 
 
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 The romance between Blake Lively and Ryan Reynolds is heating up. 
 
 Although the "Green Lantern" co-stars have yet to confirm they're a couple, a source close to the actors tells us their relationship is getting "more serious" - and another insider says Lively just made her second trip to Boston to visit Reynolds. 
 
 "[Ryan] really respects her," the source says, adding that the two hotties - who, last year, denied reports that they'd dallied near the end of Reynolds' marriage to Scarlett Johansson - stayed in contact throughout Lively's relationship with Leonardo DiCaprio. 
 
 The leggy Lively and abs-fabulous Reynolds have certainly been spending more time together recently. 
 
 According to another source, after Reynolds reportedly visited Lively on the New York City set of "Gossip Girl" on Oct. 8, the actress reciprocated by heading to Boston - where Reynolds is shooting the fantasy crime picture "R.I.P.D." 
 
 On Oct. 5, we first reported that Lively spent the weekend at Reynolds' Back Bay apartment in Boston just days before her split with DiCaprio was announced. 
 
 Our source says that Lively, 24, and Reynolds, who's 10 years her senior, were spotted having a romantic dinner last Monday at Mistral Bistro, an upscale French restaurant in Boston's South End. 
 
 We hear that Lively even picked up the check. 
 
 The source says Lively wanted to spend "a few days" with Reynolds, but was only able to stay one night. 
 
 She returned to New York City on Oct. 11. 
 
 Reynolds seems to have remained on her mind, however. The source adds that Lively did some serious shopping at Bergdorf Goodman's men's store on Fifth Ave. on Thursday. 
 
 The actress was spotted leaving the store with three bulging bags of clothing. 
 
 Presents for Reynolds, perhaps? 
 
 Lively didn't forget to do a little retail therapy for herself. That same day, the actress - who's the face of Chanel's Mademoiselle handbag line - dropped about $5,000 at the Chanel SoHo boutique. 
 
 A spokeswoman for Lively did not respond by our deadline. 
 
 Although Reynolds and Johansson never publicly cited the reason for their divorce, which was finalized in July, the Lamborghini-curved Scar-Jo recently told the German magazine Gala that she can be "overcritical - with myself and with other people" and "incredibly impatient - regarding my job, my family and men." She added: "I want things to progress. I hate stagnation!" 
 
 As for Lively's ex-beau DiCaprio, he's recently been linked to Australia's "Next Top Model" Alyce Crawford, although Crawford has said they're "just friends." 
 
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– Apparently that dinner with Bradley Cooper last month was no fluke: Jennifer Lopez was spotted with the Hollywood heartthrob again in LA Saturday, and People has pictures. “She likes him,” says one source. Another adds, “It makes her feel good that he seems so into her. She has a fun time with Bradley and he makes her laugh.” In more rebound news, Blake Lively has moved on from Leonardo DiCaprio to ScarJo ex Ryan Reynolds, and sources tell the New York Daily News that their relationship is getting “more serious” as Lively recently visited Reynolds in Boston for a second time. As for her ex, Leo is filming The Great Gatsby in Australia and “has six local models on speed dial,” the Sun reports.