The USA international joined Leeds on loan from Villa Park last season and he made 16 Championship appearances as Grayson's troops finished just outside the play-off places.
Lichaj operated in both full-back positions and Leeds' manager liked what he saw from the 22-year-old, who is seen as one for the future by Villa.
The club now have a new man at the helm in ex-Birmingham boss McLeish and Grayson is keen to ascertain whether the Scot would be willing to let the defender depart on loan once again.
"Eric did really well last year and it could be an option if Aston Villa allow us to go down that route again," said Grayson. "But the new manager (Villa's Alex McLeish) might want to keep him there.
"If we're going to go with the loan scenario then I'd want the loans to be for the whole season. Then you know that you've got the player for that length of time.
"But the problem is that most clubs are reluctant to let fringe players out too early, unless they're really not figuring at all in pre-season."