Leeds have until Monday's 5pm deadline to either strike permanent agreements or extend the loans of Richard Naylor, Lee Trundle and Carl Dickinson until the end of the season, although all of the deals could be extended to a maximum length of 93 days after the window closes.
The latter option, however, would not allow them to remain with United until the conclusion of the current campaign.
Grayson said: "I'd like to try and extend the deals we've got with these three loan players, whether that's on permanent deals or by extending (their loans) until the end of the season. We'll have to speak to their respective clubs.
"They're other clubs' players and we have to respect that but I hope we can do deals with them because I'd like to keep them. If we're trying to extend their loans until the end of the season then we'll have to do that before 5pm on Monday. Ideally, I'd like to have it done by then."