Villa are set to open their Premier League campaign against Fulham on Saturday.
Wales international Collins is a slight doubt for the game as he is nursing a back problem.
He was forced to pull out of midweek international duty as a result of the injury and has returned to Villa Park for further treatment.
McLeish admits the centre-half faces a race against time to face the Cottagers this weekend, but believes a period of rest will have the defender ready and raring to go.
He said: "We hope he (Collins) will be ready. We have high hopes that James will be okay.
"He did suffer a back problem which resulted in the missing of the Braga game (Villa's final pre-season friendly) and withdrawing from the Wales squad.
"We thank the Welsh FA for their co-operation in this."