Morgan Stanley may pay up to $1 billion and promise to strengthen its internal controls to resolve a U.S. probe into how it handled private stock sales.

Federal investigators have spent more than four years examining whether Morgan Stanley improperly tipped off favored hedge-fund clients to big blocks of stock coming on the market. The bank fired several employees and pulled back from the block trading business, losing market share to rivals.

A possible settlement with Justice Department and Securities and Exchange Commission involves a fine of between $500 million and $1 billion, and the company may also admit that it didn’t properly oversee its employees and commit to specific compliance changes, but likely wouldn’t have to plead guilty to a crime.

JEFFREY NEWMAN IS A WHISTLEBLOWER LAWYER . HE CAN BE REACHED AT JEFF@JEFFNEWMANLAW.COM OR AT 617-823-3217