Marsh was let go by Liverpool last month along with assistant coach Colin Pascoe, with the Reds electing not to renew his contract.
A former Reds midfielder as a player, Marsh had been on the coaching staff since 2011, and ESPN described he and Pascoe as 'fall guys' for the failings of Brendan Rodgers last year.
The Mail's report confirms it is a coaching role for which he could take on at Sheffield Wednesday.
The Owls fired permanent manager Stuart Gray last month and have to yet to appoint a replacement. The Sheffield Star reported today their plan is to bring in Carlos Carvalhal as general manager and Swindon boss Mark Cooper to work alongside him as head coach.
Any decision on Marsh's future is likely to factor into the plans of both parties, with it possible Cooper could look to bring in his own coaching staff.