Three points against David Moyes' side will represent a sixth successive win for City and emulate their achievement of the 1958-59 campaign.
McLeish is determined not to repeat events of two years ago when he failed to bring in the required number of players in January 2008 to give Birmingham a realistic chance of avoiding relegation.
And he will have the promise of £20-£40million to spend from new owner Carson Yeung in making sure Blues do not suffer a similar slump to Hull who faded in the second half of last season.
McLeish said: "January is the key for me, to bring in two or three players who can help us enhance the quality of the squad.
"We will need them for a rainy day - if somebody is suspended or injured. Then we will definitely have the cover there to put them in.
"We will continue to be prudent in the choice of players and the spending.
"But I will look forward to the second part of the season and the January window.
"Sometimes it can be a burden but I felt the last time we were in the Premier League, two years ago, we never added to the squad and that cost us."
McLeish is keeping his cards close to his chest about any possible signings but has a number of potential captures on his radar.
He said: "I'm not going to name any players publicly. We have a number of lists and players under scrutiny. We will continue to do that diligence.
"We are not down the road yet where we have enough knowledge about transfer fees or wages or that kind of thing - but we are sowing some seeds."
McLeish places high demands on his players in terms of work-rate and commitment but does not feel he has to change the line-up against the Toffees.
He said: "We don't really have the capacity to do the rotation stuff, as yet. The reason for not doing it (making changes) is that the players are very confident.
"They seem to still have a spring in their step. I don't see any signs on the training ground of fatigue. We will persevere with these lads who have done so well.
"Also when you are winning, you don't feel tired. It's a psychological thing, down to the chemicals, however it works, in terms of your body and your brain.
"But the mind is such a powerful tool in life. If the players are playing with confidence and getting results, they almost feel invincible.
"Goodison Park is formidable place to go to but we will go there the way we went to Old Trafford, the Emirates Stadium, White Hart Lane, Anfield - believing in ourselves."
McLeish is set to name an unchanged line-up for the sixth successive match.
The last time City went half a dozen games with the same line-up was during the 1998-99 campaign.
McLeish has no fresh injury worries or concerns about the fitness levels of his side as they prepare for their third game in eight days.
David Murphy, Teemu Tainio, Martin Taylor and Garry O'Connor remain long-term injury absentees.
Barclays Prem W/out Top 4 2009/10 Win Outright: Birmingham 66/1