The 'Hot Right Now' hitmaker, who is in a relationship with DJ Calvin Harris, met 53-year-old Cowell at his mansion in Beverly Hills, Los Angeles, reported Daily Mirror.
"Rita was not there for dinner. She was there for a meeting and there were business colleagues with her," a spokesman for Cowell said.
The pair have been in talks about a possible role on the series following her appearance as a guest judge alongside Tulisa Contostavlos, Gary Barlow and Louis Walsh on the UK talent contest in May last year when she turned up to oversee auditions at The O2 Arena in London.