The singer is said to have signed up to play Potts's friend's partner in the biopic, alongside James Corden and Julie Walters.
"Even though Jessie's primarily a singer, she has a real talent for acting too," a source told the paper.
"Producers know she works great on camera from being on The Voice. The script looks set to be hilarious too - it's really cleverly written and has a typically British sense of humour to it."
Former mobile phone salesman Potts won the first series of Britain's Got Talent in 2007 with his rendition of opera aria 'Nessun Dorma'.
Filming for the Harvey Weinstein-produced project is due to commence next month in Swansea and the Port Talbot area in South Wales. Corden is expected to take the lead role and Simon Cowell is rumoured to be making a cameo appearance as himself.
It is hoped that production on the as-yet untitled movie will be completed by Christmas.
Jessie J's spokeswoman refused to comment on the alleged role. The 'Pricetag' singer made her acting debut at the age of 11 in a West End production of Sir Andrew Lloyd Webber's Whistle Down the Wind.
She is currently a coach on BBC talent show The Voice and is said to be recording a follow-up to her 2011 debut LP Who You Are. She is due to release her first autobiography, titled 'Nice To Meet You', on September 27.
Watch the video for Jessie J's latest single 'Laserlight' below: