SETTLED: Actress Penelope Cruz, 27, is closing on a new apartment in downtown Manhattan but is not closing the door on her relationship with her “Vanilla Sky” costar, Tom Cruise, 39, reports USA Today. Representatives for the couple say there is no truth to recent tabloid reports that they are splitting up. Cruz and Cruise have been living in his Beverly Hills home, though she has said over the past year that she also needed a place in New York . . . INVITED: Fox News anchor Greta Van Susteren, 47, is bringing rocker Ozzy Osbourne, 53, and his wife, Sharon, to the May 4 White House Correspondents’ Association dinner with President Bush, reports USA Today. The event attracts stars from Hollywood and Washington. Osbourne, who stars on MTV’s surprise hit “The Osbournes,” is scheduled to be interviewed Tuesday night on Van Susteren’s show, “On the Record” . . . INVESTIGATED: Police in Phoenix are looking into allegations that Mike Tyson, 35, assaulted a stripper, 25, and her boyfriend, 23, after an argument at a local topless bar, the Hi-Liter Gentlemen’s Club, officials told Reuters. “The investigation is ongoing, but Mr. Tyson adamantly denies assaulting anyone,” said Tyson attorney Darrow Soll, who claims to have recorded statements from witnesses backing the boxer’s story . . . DIED: Western and war movie actor John Agar, 81, best known as Shirley Temple’s first husband (in a tempestuous marriage that lasted from 1945-49), died Sunday at Providence St. Joseph Medical Center in Burbank, Calif., hospital secretary Linda Willeford told the Associated Press. Agar’s spotty career (which included the John Wayne movies “Fort Apache” and “Sands of Iwo Jima”) was cut short by alcoholism. In later years he sold real estate and insurance.