Mayer and Simpson in 2005
Lester Cohen/WireImage
"They're fond of each other. There's a flirtation," says a source close to Mayer.
They are "enjoying each other's company and seeing how things go," adds a Simpson source. "There's no title to their relationship."
On Saturday, the two were spotted clubbing in L.A. and have become regulars at Paradise Cove Café in Malibu.
Mayer, 29, and Simpson, 26, began getting friendly back in June, when they ran into each other at New York City nightclub the Double Seven.
Simpson has been easing herself back into the dating world following her 2005 split from husband Nick Lachey.
For his part, Mayer told PEOPLE this summer of his romantic life in general: "I'll be willing to give up anything at any time in my life for the right thing."
Whatever their bond may be, it’s about to go long distance: Mayer is back in L.A., and Simpson begins filming Blonde Ambition in Louisiana on Monday.
