Whatever their status, the two have been hanging out a lot as they have been gearing up for press duties for The East, which is currently in theaters in limited release.
Alexander had dinner with Ellen and their costars in NYC last month ahead of the film's premiere.
Unnamed representatives for both sides denied the two were dating at the time, and Page has not admitted to bearding specifically (though she admitted, “I’m tired of hiding.
The 27-year-old actress made the revelation in a speech at the Human Rights Campaign's Time To THRIVE conference in Las Vegas in February (14), sparking a wave of supportive messages from her Hollywood pals.
Now Skarsgard, who was wrongly rumoured to be dating Page after they met on the set of the 2013 thriller, has spoken out to congratulate her for taking the brave step.
's Alexander Skarsgard and Ellen Page ramped up romance rumors over the weekend when director Zal Batmanglij tweeted a photo of the pair sharing a warm embrace on Saturday, June 8.
The picture features Skarsgard draping his right arm over Page's shoulder and giving her a kiss on the head.
It's also unclear when the picture in question was taken.