Brian McDermott is thought to be willing to send out Morison on loan as the Leeds manager looks to make room in his squad for new signings.
McDermott admitted on Thursday that he is ready to wheel and deal in the transfer market this summer after revealing he will have to let players go if he is to bring any in.
Leeds are thought to be close to securing a move for Noel Hunt and McDermott is believed to be willing to let Morison go out on loan in a bid to get the former Reading forward's move to Elland Road over the line.
Morison only joined Leeds from Norwich City in January as part of the deal which saw Luciano Becchio move to Carrow Road and he signed a three-and-a-half year contract.
The 29-year-old scored three goals in 16 appearances for Leeds last season, but McDermott is now considering letting him move on so that he can bring in his own signings.
Millwall boss Steve Lomas refused to rule out a move for Morison last week as he continues his search for striking reinforcements and a season-long loan deal is thought to have been agreed.
Morison scored 40 goals in 95 appearances for the Lions between 2009 and 2011 and he is a big fans' favourite at the Den.