Saints lifted the trophy seven times in the first 13 years of Super League but they have endured a barren run since their 28-16 win over Hull at Wembley in 2008.
Woolf is hoping for a first win in the famous knock-out competition after Saints went down 20-18 to Warrington in 2020, his first season at the club.
The reigning Super League champions take on Cup holders Leeds at the Totally Wicked Stadium this Saturday.
Woolf said: “As soon as the draw was made, there was a real excitement among the players.
“Leeds obviously had some success last year and we get the opportunity to play the Challenge Cup champions. That usually comes a little bit later I suppose but we can’t wait for the game.
“The fact that we haven’t had success in this competition for a very long time hasn’t been lost on us.”
Agar is now in charge of the Leeds team which stands in the way of Woolf’s men in Saturday’s eagerly-anticipated third-round clash of the league champions and Cup holders.
Agar said: “I think it’s the toughest draw you can get, there’s no ducking away from it.
“Kristian and his team have been a real benchmark team for a fair period of time and they’ve had an impressive start to the season.
“One thing that did surprise me is that it’s been a while since they’ve actually won it, given the success that they’ve had.
“As I was the losing coach at Wembley that day (2008), I hope that’s not an omen.”