Goalkeeper Given and defender Dunne played a major part in helping Ireland reach the Euro 2012 finals by overcoming Estonia in the two-legged play-off. The pair have enjoyed a new lease of life this season and now McLeish hopes they can "bring a touch of magic" to Villa when they resume action at White Hart Lane after a 17-day lay-off.
The Scot said: "I'm delighted for Shay and Richard. They are two terrific professionals and Ireland have waited a long time to get to a major tournament. I'm a bit jealous for the sake of my own country. At the moment we are looking for the Irish lads to bring a touch of the magic to Villa."
He added: "I said to the lads to bring some of that spirit and winning feeling back to the club and give it to the rest of the lads.
"I said 'sprinkle the magic on them' and there is a feelgood factor from that point of view.
"They will have that feeling of mental toughness and invincibility. If that filters throughout our team, then it is going to be great for the rest of the lads."
Dunne fell out of favour under McLeish's predecessor, Gerard Houllier, while Given moved from Manchester City in the summer after not being content to remain as number two to Joe Hart.
McLeish said: "Certainly their performances have been great. Shay has been a very settling influence in the team and in the squad and Richard's form has been terrific.
"Goalkeepers and defenders are probably the most consistent performers in the whole season and they need to be. These two have been part of the reason for the steady start we have made."