According to The Independent, Gerrard has held discussions with new Liverpool manager Jurgen Klopp.
It has been reported by the British newspaper that the duo have spoken to each other several times on the telephone since last month.
The Independent claims that at the moment the talk is about Gerrard training with Liverpool until January 15 when he is due to return to the USA to rejoin his club Los Angeles Galaxy.
The Major League Soccer outfit are not willing to sanction a loan deal, according to the report, and will demand a transfer fee if Liverpool want to sign Gerrard in a playing capacity.
Fjortoft believes that signing the former England international midfielder in a playing capacity would not be a good decision from Liverpool, but he has suggested that the 35-year-old could be given the role of an assistant coach under manager Klopp.
I love Steven Gerrard. One of the best I've seen live. But take him back to Liverpool now would be a big mistake. If so: As assistant coach— Jan Aage Fjortoft (@JanAageFjortoft) November 4, 2015