The pair have met several times, and Cowell even invited Griffiths, 34, to his 14 million pounds Beverley Hills mansion to celebrate his 53rd birthday, reported Sun online.
"She and Simon have started to get very close. It is early days but there is certainly a chemistry between them," a source said.
Griffiths, a singer and songwriter, started dating F1 ace Button in 2000. They announced their engagement three years later, shortly after she left the BBC's Fame Academy talent contestant.
But in 2005 they called off their wedding with just three months to go. Friends said that the break-up was mutual, but Griffiths is thought to have been keen to start a family.
Meanwhile Cowell has had relationships with stars including singers Sinitta, 48, and 40-year-old Dannii Minogue.