The new Villa boss was hoping to land one of his transfer targets before the weekend so that they had time to bond with the rest of his squad but has been frustrated in his attempt to sign Charles N'Zogbia.
Wigan rejected a bid earlier this week, forcing McLeish to draw up a list of alternatives if he fails to capture the French winger.
That is believed to include Fiorentina's Juan Manuel Vargas, although any new arrivals are not expected at Villa Park this week.
"It would be nice to think we can add another player before we go away at the weekend," McLeish told Sky Sports News.
"The hopes of that look slim but we are still in the market for another player.
"We've already got a list so I don't think we'd be caught short if our first target didn't happen.
"We'll keep looking at the options available to us but it's still early in terms of the pre-season games so we'll have to suck it and see at the moment."