Disley was forced to sit out the Football League opener against Morecambe and Tuesday's EFL Cup tie at Derby after suffering concussion in the pre-season game at Gainsborough Trinity.
Speaking on Mariners PlayerHD after that cup tie at Derby, Paul Hurst said: "He came in for a session yesterday and then he'll probably have a non-contact day today.
"Then I think we can get him back involved potentially for the weekend."
The Town boss now has concerns over the fitness of Sean McAllister after the midfielder limped off on Tuesday night. The gaffer added: "Sean was feeling his groin – he didn't particularly volunteer to come off, but I think he's one of those pros that wouldn't have come off unless we made him.
"I think it was for the best with an eye on Saturday and hoping to have him available.
"It wasn't something he screaming or shouting about, but he was seeing Dave Moore at half-time and he didn't look like he was moving quite right to me."