The 22-year-old left Leeds in 2009 to join up with Aston Villa for an undisclosed fee.
However, the midfielder is now believed to have been made available for loan by Villa boss Alex McLeish.
Grayson has revealed his admiration for Delph, but stopped short of confirming that he would be making an offer for the Bradford-born player.
"Fabian Delph is a good player who knows about Leeds United because he has been here before," he told the club's official website.
"His name is being bandied around as if he is available for loan. You're not going to draw me on whether we will do it or not, but he's a player, along with others, that would fit the bill.
"He fits the bill because he knows what this club is about and what it means to play here, but we're working towards one or two deals and I will refuse to name them."
Delph made almost 50 appearances during his first stint with Leeds.