Rumours about the nature of their relationship have been swirling for some time, but it's being reported that things 'seem to be heating up' between Johnny Depp and Amber Heard. The Rum Diary co-stars are said to be so close that bisexual actress Heard, 26, has been a 'regular visitor' to the New Mexico set of The Lone Ranger where 49-year-old Depp is currently filming. And Johnny, who made an official announcement that he had split from partner of 14 years Vanessa Paradis on Tuesday, is even said to have bought Heard a horse so they can ride together, according to a report in Globe magazine.A source claims Depp is smitten by the Hitchcock blonde, and reportedly said:' When I first saw Amber, it was like seeing an old-time movie star like Lauren Bacall.'The American actress who was born in Austin, Texas, previously worked as a model and before starring in The Rum Diary alongside Depp had had small roles in a number of films.While she was raised a Catholic, after the death of her best friend died in a car crash Heard declared herself an atheist.Heard has described her role as Johnny Depp's love interest in the film, The Rum Diary, as 'the best experience of my life.'She gushed to magazine Dazed about Depp: 'He’s such a wonderful presence; he is enigmatic and compelling and a true artist, seriously intelligent and incredibly sensitive. 'Everybody on set respects and likes him, which says a lot about an actor. It’s a grueling job at times and the stress level that everybody feels in the industry is intense – but it doesn’t affect Johnny.'It seems like he has time to look everybody in the eye and I like that, it was wonderful to see.'Despite Johnny's denials, a number of publications carried pictures and reports that he and Heard enjoyed a trip together to Las Vegas on a private plane.Vanessa and Johnny had not been pictured together in public for months, but the Dark Shadows star insisted last month that there was no truth to talk of a split.