BOSTON – Gov. Mitt Romney said Tuesday he is weighing an unusual plan that could allow the state to reap hefty gambling profits without the hassle of building casinos.

The plan, which could bring in tens of millions of dollars, would allow the state to auction off the rights to build casinos in Massachusetts with the understanding that the casinos would never be built.

The auction would be targeted at casino owners in neighboring states who would be willing to pay big money to block competition.

It’s estimated that Massachusetts residents spend as much as $250 million each year at casinos in Connecticut and at race tracks in Rhode Island and New Hampshire.

Lawmakers have been looking at casino gambling in Massachusetts as a way to help the state out of its fiscal crunch.

Romney said the plan under consideration would let the state bring in gambling revenues while avoiding some of the headaches that critics say come with casinos.

“It is something that is a creative, possible source of revenue,” Romney said. “[I] would relish the opportunity of finding tens of millions of dollars coming to Massachusetts without our having the additional social costs associated with additional gambling within our borders.”

Some legislative leaders quickly endorsed the idea.