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.''
'The Now Now' will be released on June 29th, and two new teaser tracks have appeared - 'Humility' and 'Lake Zurich'.
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