The Villa boss feels the Gunners will be the team under pressure and their players aware of the need to halt their recent poor run of results.
McLeish also has the memory of triumphing over Arsenal in last season's Carling Cup final when Birmingham boss while Villa won 2-1 when they visited the Emirates Stadium last season.
But the Scot knows Villa will have to be at their best if they are to spring a surprise result despite Arsenal's current lengthy injury list.
McLeish said: "I don't see why we should be fearing Arsenal. I am sure the lads will remember what they have done at the Emirates before.
"Statistics don't determine the outcome of this latest encounter but it does offer the players evidence they can do it against the best of the Arsenal teams.
"There is a good bit of confidence going into this next game. It's the FA Cup, we are away, the pressure will be more on the home team Arsenal to win.
"I'm sure they are under pressure with the fact they've lost two or three games. You rarely see the top clubs losing four in a row.
"But at the same time we are not going to be shouting from the rooftops 'we're going to do this, we're going to do that.'
"We have to be at our best defensively because they have some great attackers - but we have attackers ourselves who can also hurt people."
McLeish intends to field his strongest available side against Arsenal even though they have a home league game with QPR to contend with before a visit to Newcastle next weekend.
He said: "The magic of the FA Cup dictates you can't leave anything to chance and you have to go and do your utmost to get through to the next round.
"We have a tough away tie but the top clubs have proven this season that they are not unbeatable.
"I'm not thinking of anything other than putting out my strongest team this weekend.
"We should be able to cope. There are three days before the next game and we have players in a good confident mood.
"I don't think any of them would be too happy if I let them out this weekend and rested them."
McLeish against reiterated he is unlikely to add any more players before the transfer deadline and has faith in the club's youngsters such as midfielder Gary Gardiner.
He made his full debut in last weekend's win at Wolves and coped with being switched from a central role to a wider position after a half-time reshuffle.
McLeish said: "I've totally ignored the transfer deadline. I keep saying we've got a wage bill to manage and we've not really wavered from that.
"The youth policy, and players like Gary Gardner will get their chance, and hopefully grow up very quickly in this demanding league of ours."
