Nicole Kidman and Lenny Kravitz may be getting serious about their house hunt. The pair has now made several trips to inspect a five-story, 11,000-sq.-ft., 21-room neo-French townhouse on Manhattan's East Side, reports TV's "Access Hollywood," following up story leads first reported in PEOPLE.

The house, which used to be part of a school but is now set to be converted back into a single-family dwelling, carries an asking price of $18.5 million. "Access," however, quotes Kidman as reputedly having said she finds the place just too big.

The Douglas Elliman real estate firm, which also is handling the sale of Kravitz's downtown bachelor pad for $13.95 million, is handling the townhouse transaction, says the New York Post. According to the listing for the property, the 1920s-era building -- located in the 70s between Fifth and Madison avenues -- has all its original architectural details intact, including a grand marble reception hall, with central staircase, and private garden.

"Access," which even showed the elevator inside the house, points out that the residence also has 10 bathrooms, which should be more than enough to accommodate Kravitz, 39, and Kidman, 37 -- not to mention her two children, Isabella, 10, and Connor, 8, whose father is Tom Cruise.

The Post, being cheeky, also mentions that should things between Kravitz and Kidman not work out, the rocker has the advantage of having newly single socialite Alexandra von Furstenberg as a next-door neighbor should the house sale go through.

Reps for Kidman and Kravitz had no comment.