The former Southampton boss only took charge at Ibrox over the summer but a 1-1 draw with Falkirk ultimately proved the final straw, leaving the Gers languishing in eighth place with just eight points from seven league games.
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According to journalist Ben Jacobs, Gerrard is no longer interested in taking up the managerial role at Ibrox Stadium.
The report adds that the English great is not currently ready to take on a new managerial assignment.
Although he held positive discussions with the Scottish club and an agreement was close to being finalized, both parties have now mutually ended talks though the door remains open for potential future discussions.