Coutinho left Philips Stadion at the end of last season after coach Guus Hiddink opted not to extend the youngster's contract.
The 20-year-old spent the closing months of last term on loan at Den Bosch but has thus far been unable to secure a fresh club.
He has linked up with NAC at their pre-season training camp in Mierlo and is expected to feature in a brace of friendlies.
During his stint with PSV, Coutinho made a handful of Eredivisie appearances and plumped for the Dutch giants ahead of NAC when it came to his footballing education.
