The 18-year-old, who has recently spent a loan spell in the Evo-Stik League with North Ferriby United, has joined the Pilgrims in pursuit of regular first team football.
Mulready was handed a professional contract by Rob Scott and Paul Hurst at the end of last season, although he is yet to figure competitively for the Mariners this campaign.
Subject to the paperwork being rubber-stamped, Mulready will be available for Saturday's trip to Altrincham.