According to Heat, the X Factor boss is attracted to the woman he hired from the Strictly Come Dancing panel for his own show.
"Simon thinks she's beautiful," a supposed friend told the magazine. "He's always complimenting her hair, and her hands.
"As soon as he saw her on Strictly he knew he wanted her for BGT, and he even sent her 20 white roses to charm her."
They added: "Since they've been working together Simon's become even more keen.
"He's really turned on by feisty, gutsy women. Like Cheryl [Cole], Alesha bounced back from a painful divorce and Simon thinks she's really something."
Tom Bower's unauthorised biography of Cowell claims that the show boss had a fling with Dannii Minogue. The affair was later confirmed by Cowell's PR agent Max Clifford.
Cowell was also said to be "mesmerised" by Cole and "would have liked an affair" with her, prompting claims that she would reveal all about him in her own book.
> Simon Cowell: 'Alesha Dixon Britain's Got Talent signing was BBC dig'
> Alesha Dixon denies Amanda Holden rift: 'We're really close friends'
Photo gallery - Alesha Dixon and Simon Cowell on 'Britain's Got Talent'