The 37-year-old actor and Shipp, who is 13 years younger than him, got close while filming the "X-Men" movie, reported Daily Mirror.
"It's no great secret how they've got close. James has been quite open among the cast and crew that his marriage was over and it seems he has struck up a friendship with Alex since then," a source said.
The insider added, "It's been the source of some gossip among those connected to the film - but they've kept things low key."
The source additionally claimed that McAvoy and Duff's marriage had been in crisis for some time, but they're still living together in their house in north London.
"He told people things had started to break down some time ago but that everything was fine and they were perfectly happy."
The estranged couple was seen enjoying a bike ride on Sunday, May 15. They have one child together, five-year-old Brendan.
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