Morris, who has come through the youth ranks at the Banks's Stadium, has been a regular for the Saddlers over the past few years.
But the 24-year-old has found playing time harder to come by this season.
Morris has started 17 games and featured 26 times under Dean Keates during the 2018/19 campaign.
But despite having scored five goals – a career best – he has often had to play second-fiddle to other forward players in the squad.
A number of clubs are now understood to be monitoring his situation with Tranmere Rovers leading the chase.
Micky Mellon's side are currently 10th in League Two and hope Morris will add goals and assists to push them into the play-offs.
Morris is out of contract in the summer and now has to decide if he wants to effectively end his Walsall career six months early by moving to Prenton Park on loan.
But while he could stay at the Banks's Stadium and fight for his place, manager Keates has gone on record to state he is chasing attacking reinforcements before the transfer window closes.
The boss is believed to want at least one more addition before Thursday's deadline.
And that would see Morris' opportunities restricted even further.