Manchester City boss Mark Hughes is the latest Premier League boss to express his interest in signing the highly-rated England Under-21 international.
Tottenham are also monitoring Delph, while Aston Villa and Everton are reported to have had bids rejected over the summer.
Grayson has revealed two top-flight clubs have failed with offers for Delph, who has been rated in the £10million bracket.
The Leeds boss is prepared to accept Delph's departure for the right price and is waiting to see if anything develops before the transfer window closes.
"We've had two bids from Premier League clubs over two weeks ago that we turned down," Grayson told Sky Sports News.
"They were nowhere near the target of the realistic aim that we are looking to receive, but I know that could change at any time.
"That's football for you.
"As long as he's contracted to us he'll show and perform like he has done all over pre-season, but obviously we're aware anything could happen as well."