The 53-year-old music mogul has enjoyed a string of dates with Louise Griffiths - who was previously engaged to Formula 1 star Jenson Button until 2005 - and even invited her to his Beverly Hills home to celebrate his recent birthday.
A friend of Louise told The Sun newspaper: "It is very early days but there is certainly a chemistry between them."
After one date, Louise - a former contestant in TV talent show `Fame Academy` - tweeted: "Going to bed as the sun is coming up. Haven`t done that in a while! #fun. (sic)"
However, the brunette beauty`s pal insists the relationship isn`t serious yet as Louise is wary of Simon`s reluctance to commit to one woman.
The source added: "She knows there are commitment issues. Currently this is not serious, but the beginnings of a promising relationship."
Simon`s spokesperson Max Clifford revealed he is unsure who the TV talent show judge is currently dating.
He said: "There have been two or three very attractive ladies who people are asking about in relation to Simon - and I`m not sure of any of them."
The `X Factor` chief was recently romantically linked to Carmen Electra.
He got engaged to make-up artist Mezhgan Hussainy in 2010 but they split a year later, and his other previous girlfriends include Sinitta and Terri Seymour.
Simon - who is known for remaining close to his former girlfriends after they split - previously admitted he likes to see the women in his life "fight".
He said: "Every girl wants to be number one and they`re very territorial.
"I like the fight, because otherwise I`d have a dull group of girlfriends."