According to reports published in Globe, the actress has been making regular visits to the set of Depp's latest flick The Lone Ranger, in Mexico, where things 'seem to be heating up'.
In fact the magazine even alleges the actor has bought a horse he can go riding with Heard, so enamoured is he with the blonde beauty.
Rumours of a romance between the pair began doing the rounds earlier this year, when Amber was spied boarding Johnny Depp's private plane in Las Vegas.
Talk was further fuelled by reports Depp's relationship with Vanessa Paradis was on the rocks.
Despite fending off rumours of a break-up earlier this year, a rep for the Hollywood super-couple, who have never married, yesterday confirmed the pair have 'amicably separated'
'They have amicably separated,' a statement from their official spokesman read. 'Please respect their privacy and, more importantly, the privacy of their children.'
Today some are reporting Depp has agreed to pay Paradis £100 million following the split, revealing the pair remain on good terms for the sake of their children.
What are your thoughts on the latest romance rumours? Is Johnny Depp really dating Amber Heard? Let us know in the comments box below…