BOSTON — Federal prosecutors are trying to freeze the assets of mobster James “Whitey” Bulger’s girlfriend to cover any fine she may be ordered to pay when she is sentenced for helping Bulger evade authorities for 16 years.

They have asked a judge to order a garnishment of any assets belonging to Catherine Greig held by Eastern Bank, according to court documents.

In the filing, Assistant U.S. Attorney Christopher Donato says prosecutors believe Greig “holds significant assets and/or funds.”

Greig pleaded guilty last week to helping Bulger avoid capture since 1995. Bulger has pleaded not guilty to participating in 19 murders. The couple was captured last summer in Santa Monica, Calif.

Donato said he believes there’s a strong likelihood Greig will be ordered to pay a fine when she’s sentenced in June. He has asked a judge to order any Greig asset held by Eastern Bank to be paid to the government if a fine is ordered.

During a hearing in U.S. District Court on Monday, Greig’s attorney, Kevin Reddington, said Greig does not plan to transfer any property or funds.

“The money will maintain a status quo … and the same thing with the real estate,” Reddington said. “It’s not going anywhere, I assure the court of that.”

During a separate hearing Monday in Bulger’s case, a judge told prosecutors and Bulger’s lawyers to cooperate as the two sides continued to spar over the voluminous amount of evidence expected to be used at Bulger’s trial.

Bulger’s attorneys have complained that prosecutors have turned over a “mountain” of disorganized documents.