Republic of Ireland international McGrath rejected a pre-contract offer which it is understood would have made him one of the Dons’ highest paid players. The 25-year-old is believed to prefer a move to English football.
While Glass declined to comment specifically about McGrath, he expressed confidence that Aberdeen can attract players with the necessary attributes to improve his squad.
“We want players that want to come play for Aberdeen,” said Glass. “There is a pressure that is attached to playing here at this club.
“We are hoping that the targets we go for can see what we offer them for their careers. It’s a brilliant club to play for and I’m sure we will get the right people in the door.
“We have targets we are looking at, whether that be for this month or the summer. We need to make sure anything we bring in will strengthen and we talk about that continually.
“It’s important that we are in a position where we are not doing anything panicked last minute either. It is all targeted.
“If we can get the right ones, we will. If we can’t, we won't bring in bodies just for the sake of it. That’s really important.
“We have young players whose pathways shouldn’t be blocked and in general we have a good squad as it stands.
“We don’t have to lose anyone unless things go outwith our control in terms of ridiculous money coming in for any player. Until anything like that comes on your table, we are very happy with the squad we have got.”
Glass reported no fresh developments regarding the futures of his highly-rated right-back Calvin Ramsay, who has been linked with a host of major clubs including Bologna, Eintracht Frankfurt and Newcastle United, and attacking midfielder Ryan Hedges who is out of contract at the end of the season.
But Glass knows the 18-year-old, under contract at Pittodrie until 2024, could attract attention again as Aberdeen return to action after the winter break with their live televised home game against Rangers on Tuesday night.
“There’s not (any further interest in Calvin) but I don’t know if that will kick up now that the games have started again,” said Glass.
“Obviously, we have a high profile one like Rangers. It’s the same situation as it was previously with Calvin. We are in control of the situation.
“It is also the exact same situation with Ryan, as in we have had zero contract from any club asking to talk to him. Which is surprising.
“If nothing happens, nothing happens and our squad will be strong for the second half of the season.
“People do their work in the background and might be looking at our players and hit you with a bid late. I’m sure there are still plenty of people interested in a lot of our players.
“However nothing has changed there. We have contingency plans for everything. But until something happens, nothing happens.”