Grayson offered hope to Alan Sheehan, Andy Robinson and Lubomir Michalik - all of whom have waited for almost four months for moves out of Leeds - by stating that interest in them was likely to increase before the transfer window closes.
The three players were made available by Grayson at the end of last season, along with striker Tresor Kandol.
Leeds agreed to terminate the remainder of Kandol's four-year contract this month after failing to find a new club for him, but Sheehan, Robinson and Michalik remain on the books at Elland Road with the summer window set to close in little more than 48 hours time.
Grayson said: "They're good lads, they've trained hard and they've done what's been asked of them but it's in their interests to play football. They know they won't play many games here. I'm sure there'll be one or two inquiries before Tuesday."
Swindon were expected to pursue Sheehan's signature after taking the left-back on loan last season, but a permanent switch to the County Ground has not developed while interest from Swansea City failed to lead to a move.
United's manager revealed that he had received no offers for any of his senior players, despite rumours of interest in certain professionals.
Scottish Premier League club Celtic were said to be monitoring Luciano Becchio, whose contract at Elland Road is less than 12 months from expiring, but Grayson said he would not invite or entertain any attempts to capture key members of his squad.
"I've had no phone calls about players who are in the team or out of the team," he said. "That might change in the next few days but I'm certainly not looking to sell any player who is in my team.
"The only ones I'm looking to let leave are the ones who've been available since the start of the summer."