Becchio demanded a transfer earlier this month, and he has attracted attention from a number of clubs.
Leeds have rejected bids from the continent, but now a deal with Norwich looks to be close, with Morison included as part of the package.
With the deadline coming in little over 24 hours, Sky Sports understands both players are heading in the opposite direction for talks.
Becchio has scored 19 goals for Leeds this season and has two years left on his current deal - but talks over a fresh contract have stalled.
Morison has made just four starts this season after Chris Hughton took charge at Carrow Road.
Sky Bet suspended betting on Becchio's next club on Wednesday afternoon following a string of bets for him to join Norwich at as short as 1/10.