Delph was regarded as one of the brightest young prospects in the country when he moved from Leeds to Villa as a 19-year-old two seasons ago.
But he has not established a regular spot at Villa and has also suffered several injury setbacks and is currently recovering from an ankle problem.
McLeish said: "I think it's time for Fabian Delph to show the reason why Villa invested a decent sum of money on a very young player.
"The challenge is there for Fabian. He can certainly tackle as well as pass the ball. He's got that quality.
"He's got a determined attitude and believes in himself."
McLeish will use pre-season - Villa report back on Friday - to determine whether Delph is ready for the Premier League.
He said: "We'll get a good idea in pre-season and will assess him then. I have to assess if he is ready for the Premier League.
"But for him, after his injury problems, to get a full season would be a massive boost to his mental toughness."