The marriage, less than six months after she and actor Ben Affleck called off their wedding, has not yet been confirmed by the couple's publicists.
Lopez and Anthony had dated years ago.
It would be a third marriage for the 33-year-old Lopez. She was married to waiter Ojani Noa for more than a year in 1997 and the dancer Cris Judd in 2001 for nine months, reported Sky News.
Anthony divorced his wife, Dayanara Torres, the former Miss Universe, last week in the Dominican Republic.