Martin has been training at Rockliffe Park for the last fortnight, and impressed in a series of practice matches last weekend.
The midfielder, who was released by Blackpool in May at the end of an injury-hit campaign, is expected to sign a one-year deal with the Teessiders.
He will then travel to Slovenia to join up with the rest of Tony Mowbray's squad for the second half of the club's pre-season tour.
Boro play their opening friendly against Istanbul BB in Markovci's Stojnci Stadium this evening (kick off 6pm).
Mowbray is expected to make a host of substitutions during the game, with the majority of the squad expected to get a run out at some stage.