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"She's tiptoeing back into the dating world," a source tells PEOPLE. "It's the first stage. She's never been happier."
Mayer, 28, began a co-headlining tour with Sheryl Crow on Aug. 24, and Simpson, 26, is expected to attend his concert in Jones Beach, N.Y., on Wednesday night.
Simpson is currently in New York promoting her new album, A Public Affair, which was released Tuesday – although a bruised vocal cord has quashed any planned performances. (She did stop by MTV's TRL Tuesday and is set to appear on Today on Friday.)
Similarly, Mayer had to cancel his Hartford, Conn., appearance with Crow on Saturday due to laryngitis, the Associated Press reported.
The two singers have known each other for several years and last year both attended Clive Davis's pre-Grammys party in Beverly Hills.
Although Simpson has been linked to Jared Leto and her Employee of the Month costar and Teen Choice Awards cohost Dane Cook, Simpson has not officially dated anyone since her November 2005 separation from Nick Lachey.
For more on this story, pick up the new issue of PEOPLE, on newsstands Friday.
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
Note that this week’s cover of PEOPLE may differ regionally
