According to The Sun, she began romancing the former Royal Marine while shooting a celebrity edition of the Sky One show.
Tornado, real name David McIntosh, was spotted leaving Faces nightclub with Lloyd at the weekend.
"They could not keep their hands off each other," said a source. "But they went to extremes not to be snapped together, and Tornado got a bit shirty with the photographers."
A spokesperson for the glamour model said: "They enjoy each other’s company and are very good friends."
Lloyd's previous boyfriends include businessman Will Foster and footballers Teddy Sheringham and Jermain Defoe.