Boro are ready to offer the midfielder £15,000 a week but Newcastle also want the 21- year-old.
Digard, 21, is known as the "new Patrick Vieira” in Paris.
He joined PSG from Le Havre last year on a three-year deal but is keen on a move to the Premier League after an impressive first season in the French capital.
Newcastle are also chasing Digard but have yet to match Boro's offer.
The box-to-box midfielder has represented France at every level from under-15 to under-21.