The 'Game of Thrones' actress has reportedly started to get close to the musician, and while they're taking it slow in the early stages, it is said they ''really like each other''.
An insider told The Sun on Sunday newspaper: ''It's still early days. She has just broken into the big time through 'Game of Thrones' and James and his band are constantly travelling to gigs.
''So they're taking it pretty slowly but they do really like each other.''
The two stars started chatting on Twitter, before meeting up on a number of occasions, including meals out and a trip to the beach.
However, James' bandmates have recently admitted their touring lifestyle makes it difficult to date ''a normal girl'', meaning romances with other celebrities have a better chance of working out.
Singer Bradley Simpson previously said: ''I think you see a lot of celebs dating other celebs, because both sides can deal with the nature of the job.
''If you're in a band and you're trying to date a normal girl at university, it will be harder because of the difference in lifestyle.''
Over the past five years, Shia LaBeouf has gone from promising young actor to unemployable disaster and back again.
In Deepwater Horizon, Mark Wahlberg reteams with his Lone Survivor director Peter Berg.
The live album is set for released in November.
The movie begins filming in the UK.
Time to learn what Kathy Bates' character has to do with all of this.
X-Men Apocalypse comes as the ninth instalment in the X-Men film series and stars Jennifer...
This closing chapter of the First Class trilogy falls into the same trap as The...
Mutants and humans alike are familiar with the story of Apocalypse, he was the first...