Rafael Benitez is leaving the Magpies when his contract expires at the end of June and owner Mike Ashley is on the search for a new boss with plenty of names, including Jose Mourinho and Arsene Wenger, touted as possible replacements.
Hutchison may have played for bitter rivals Sunderland, but he has been a lifelong Newcastle fan.
He tweeted his suggestions for who he would like to see next in the dugout at St James’ Park.
He said: “Wouldn’t mind Gattuso or my fave would be S Gerrard.”
Gennaro Gattuso left his role as AC Milan’s head coach in May after 18 months in the job.
He guided the club to a fifth-place finish in Serie A in the 2018/19 campaign but just missed out on Champions League qualification.
Steven Gerrard led Rangers to a second-place finish in the Scottish Premiership in just his first season in charge.
The former Liverpool midfielder has been linked with several other jobs but appears happy with Rangers.