The mogul is attracted to the former model, who works on his TV show `Britain`s Got Talent` as assistant to judge Alesha Dixon.
Although Simon - who is believed to have split from fiancee Mezghan Hussainy earlier this year - admits he is smitten with Francesca, he hasn`t been able to pluck up the courage to ask her on a date yet.
He said: "We have the new, cutest make-upartist. But I just can`t talk to her, I`m kind of tongue-tied."
Simon, 52, was asked by `Britain`s Got More Talent` host Stephen Mulhern if he wanted him to ask Francesca out on his behalf, but replied: "No, that would make it awkward."
Simon was then teased by his fellow judge David Walliams, who told him she had a boyfriend, adding: "I hear he`s a cagefighter."
Francesca - who dated singer Craig David in 2007 - is a new addition to the `Britain`s Got Talent` team, and followed Alesha from her former show `Strictly Come Dancing`.
A source told the Daily Mirror newspaper: "She has only met Simon a few times and he hardly spoke to her. Now she knows it`s because he really fancies her."
The 27-year-old model`s friends took to twitter after hearing Simon discuss her on the show, with one saying: "Simon totes wants to get in your panties (sic)!!!"