The 28-year-old waif-like supermodel gave birth to a 6½-pound baby girl at the St. John and Elizabeth Hospital in west London early Sunday, the reports said.
Moss and Jefferson Hack, her publisher and boyfriend, are planning to call the girl Lola, according to gossip columnists in the Daily Mirror newspaper.
A spokeswoman for Moss' modeling agency, Storm, did not immediately return phone calls asking about the news reports.
Hack, 30, publisher of style magazine "Dazed & Confused," took his girlfriend to the hospital after having lunch at a Greek restaurant with actor Jude Law and his wife Sadie Frost, the Daily Mirror said.
Moss, who grew up in south London, has been modeling since the age of 14.
Previous boyfriends have included movie star Johnny Depp and Antony Langdon, a guitarist with the pop group Spacehog.