The former Leeds United youngster is out of contract in the summer and figured sparsely in the first-team this season, but although this move would imply he has no future at Glanford Park the club's manager Nigel Adkins told the Scunthorpe Telegraph that he may remain in his plans for the end of the campaign.
United will have the option to recall Morris with a 24 hour notice after the first 28 days of the loan.
Morris may go straight into the Cumbrians' squad as their influential midfielder Graham Kavanagh a doubt for Saturday's game against Northampton Town with a hip injury.