The 'Sky Full Of Stars' hitmaker was seen heading into a New York hotel with the 'Peaky Blinders' actress, fuelling speculation the pair are getting close.
A source said: ''It's early days but Chris has made a lot of effort to see her.
''Annabelle is a free spirit. Chris wants a more laid-back partner after Gwyneth [Paltrow; his ex-wife].''
The 38-year-old singer has reportedly been doing all he can to see the actress, by visiting her on the set of her latest film 'Come and Find Me' in Vancouver, Canada, before heading out with the cast for dinner two evenings in a row.
And in another grand gesture, Chris is believed to have hired a cinema and organised a private showing of 'Mission: Impossible Rogue Nation' with the help of pal Simon Pegg.
The news comes only days after sources revealed Chris had split from 'Hunger Games' star Jennifer Lawrence, 13 years his junior, for the third time.
A source told The Sun newspaper: ''[It had been] very off and on as she was so young.''
The news of the split will shock their fans as an insider recently claimed Chris was ''committed'' to Jennifer.
They said: ''Now that he's finally divorced from Gwyneth, he's finally committed to making things work with Jen. He wants her to know how serious he is about her.''
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