The X Factor boyband singer is said to have been on several dinner dates with Rithiely 'Rithy' Pereira, who appeared on BBC One's So You Think You Can Dance last year.
The Brazilian was booked as a backing dancer on The X Factor a few weeks ago, before meeting Hamblett backstage, reports The Sun.
A source said: "JJ couldn't take his eyes off Rithy the first time he spotted her backstage at The X Factor.
"They started chatting and she agreed to go out with him for a date. Now he's really into her."
Union J have reached the semi-final stage of the ITV competition after surviving the sing-off against Rylan Clark on Sunday (November 25).
The group recently stated they were proud to have improved in time, having once described themselves as the show's "weakest" singers.
The X Factor 2012 Results Show 8:
Copyright: Ken McKay/Thames/Rex Features