Delph, 22, was signed from Leeds for £6million by then Villa boss Martin O'Neill during the summer of 2009.
But he has been unable to hold down a regular first-team spot apart from a run of eight successive Premier League games at the start of this season.
McLeish said: "Fabian is one we might think about going out on loan.
"(Leeds manager) Simon Grayson did try to call me (about Delph) but I've not spoken to him yet. I think he spoke to (Villa coach) Kevin MacDonald so I'll get back in touch.
"I'm going to speak to Paul Faulkner (Villa's chief executive) to see where the club lies with it."