The actor, who played Draco Malfoy in the eight-film series, previously released some of his tracks on iTunes, and signed a record deal with Six String Productions last year.
According to The Sun, Felton and Fletcher's planned writing sessions could lead to a studio collaboration.
"Tom sounded out McFly's Tom to discuss the industry and the musical direction he wants to take," a source said. "He's a huge fan of the boys and wanted to work on a few songs."
The insider added: "There is a big chance the pair could soon go into the studio together."
Felton previously credited his band for turning some of his tracks into "credible pieces of music".
The Rise of the Planet of the Apes actor scooped the 'Choice Movie Villain' award at the Teen Choice Awards 2011 earlier this week.
> Tom Felton: 'Rise of the Planet of the Apes has strong message'
> 'Harry Potter's Tom Felton, Daniel Radcliffe 'got heated over Scrabble'
Watch Digital Spy's exclusive clip called 'The Awakening' from Rise of the Planet of the Apes below: