Representatives for the 23-year-old performer, the younger sister of actress and singer Jessica Simpson, had no immediate comment on the report and no further details were available.
Ashlee Simpson has been romantically linked to Wentz, 28, the bassist for the band Fall Out Boy, since 2006.
On Thursday the couple posted a statement at the social networking Web site friendsorenemies.com in which they announced that they would be getting married.
"We are thrilled to share that we are happily engaged. We consider this to be a very private matter, but we wanted you to hear it straight from us," the announcement said.
In addition to her career as a singer, Simpson had a role in the U.S. television show "Seventh Heaven." Her new album, "Bittersweet World," is to be released later this month.
Wentz co-founded Fall Out Boy in 2001, and the band, for which he is also the lyricist, has built a loyal following with albums that include 2005's popular "From Under the Cork Tree," which included such hits as "Dance, Dance," and "Sugar, We're Goin Down."
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