The 25-year-old left West Ham over the summer after making more than 100 appearances during his time at Upton Park and recently trained with QPR.
"He lives half-an-hour away and wants to get himself ready so I said come down and train with us," McCarthy told Town's official club website.
"Jack has actually added that extra quality to training but you have to see him in games on a full pitch.
"There's no agenda. Something might come of it, something might not."