McLeish would like to surpass the 2010-11 achievement of finishing ninth in the Premier League and challenge for a European spot.
But he is also realistic after losing several experienced players this summer, including Stewart Downing and Ashley Young, and having to reduce a sizeable wage bill.
Realistic: Villa boss McLeish says fans have to except that big players have gone
McLeish is looking for some of the club's promising youngsters, such as Fabian Delph, to make their mark plus players out in the cold under Gerard Houllier in Stephen Warnock and Stephen Ireland.
The Scot said: 'We've lost some very experienced players, don't forget, and we are looking for young players to make the breakthrough.
'That might not happen so people may have to be patient in terms of where we finish in the league. We finished very healthily in ninth position after the first half of last season was difficult.
'If we can maintain a steady progress throughout the season, that would be heading in the right direction. Would a top 10 finish would be okay? I think that would terrific. I think that would be an achievement for the players but we will try and aim higher than that.
'We lost Downing, Nigel Reo-Coker, Ashley Young and Charles (N'Zogbia) is the only newcomer in an outfield sense at the moment.
'We are relying on the old hands, some of the players who were dormant last year to come to the fore, and the youngsters to stand out. There will be opportunties for them.'
Former Birmingham boss McLeish knows the pressure will be on to bring success.
He said: 'The Villa fans want to see their team winning and I know that pressure will be on. Expectation levels at this club are a lot higher than at a lot of other clubs so I'm very much aware of that.
New face: Charles N'Zogbia moved from Wigan for ?9.5m towards the end of July
'But there has to be realism and Randy Lerner (club owner) has chosen me to do this job because he's got confidence I can do it. As an individual, that gives me the confidence we can do it together.'
Villa open their campaign at Fulham and McLeish knows striker Darren Bent will have a key role if they can replace the service he relied upon from Downing and Young.
Bent scored nine goals in 16 games after his ?18 million move from Sunderland in January and has become established in the England side.
McLeish said: 'Darren has been an immense goalscorer over the years and is now an England international.
'He is very dangerous. If we can get the right service to Darren, he will score goals. He is a great finisher. He has been doing it every day in training, in a couple of the pre-season games as well, and we just have to feed him.
'That is a role for people like Gabriel Agbonlahor, Emile Heskey, Marc Albrighton and Charles N'Zogbia.'
Bent has recovered from a shoulder problem which ruled him out of an England call-up for the game with Holland at Wembley in midweek before it was eventually called off. Central defender James Collins has also shaken off a back problem with Rangers target Carlos Cuellar (knee) the only player unavailable for selection.
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Source: Daily Mail
Source: Daily Mail