Grant played in a friendly for them ahead of the Nationwide campaign starting up on Saturday, and Glenn says:
"Paul Groves was pleased at what he brought to the friendly game he played in, where he operated at left full back and left midfield, and I think he would like to add him to the squad.
"But Paul has got his back right up against the wall at Grimsby; he has a tiny squad and the budget is nearly eaten into.
"There is very little room for movement, and he is just deciding what to do; I think he would like to bring in four or five players but can only get a couple, so he is assessing which ones - whether Grant is one of those we will just have to wait and see.
"And, ultimately, I have got to decide whether I can afford to let him go until January - and that is why I don't like the transfer windows."
Glenn feels the newly imposed system should be made more flexible, and adds:
"I think there should be a facility whereby you can loan young players of 21 and under out to the first, second, and third divisions, bring them back after a month, or leave them there all season.
"I don't like the thought of lending young players out to managers and coaches that I don't really know.
"It is difficult if you don't know how they coach and work, whereas I know that at our club I am very comfortable with the education and work they get from Roger Cross, Paul Goddard, and, obviously, when they work under me.
"We know what we are doing with our young players and it is our responsibility to give them a good education.
"But it would be much better if you had the option of bringing someone back early that you lent out if you wanted to.
"To say to a young player in August 'off you go, we won't see you until January' - I am not overly comfortable doing that."