The 72-year-old's team are 4-0 up ahead of the Tuesday's home play-off second leg with Estonia after a rampant display in Friday's first leg in Tallinn.
There will be a party atmosphere at Dublin's Aviva Stadium and the evergreen Italian coach feels more joyous scenes could follow.
"We can repeat our performance in qualification towards the World Cup in Brazil," Trapattoni told reporters.
"Now we have a strong and young team. I would be disappointed and upset if I had to leave."
Former Ireland boss Jack Charlton told Sky Sports News that the much-travelled "Trap" should be handed a new three-year deal until Brazil 2014.
"It's a great start, but it's only half-time in the tie," he told reporters.
Estonia's fairytale of winning their last three games to grab second place in Group C came to an abrupt end on Friday when they were reduced to nine men and completely outmuscled by the Irish.
Piiroja in particular will be a loss and despite being given a tough time by Ireland's Jon Walters, who netted Ireland's second goal in the first leg, he battled bravely and the visitors may now worry the Irish could run riot.
Keane scored twice in Tallinn, stabbing home a rebound from first goal-scorer Keith Andrew's free-kick and firing home a late penalty to put the tie almost out of sight.
He has now scored 53 goals in an Irish shirt and Euro 2012 could be the 31-year-old's last chance at a major international tournament.
Keane knows all about play-off heartbreak having scored in the World Cup 2010 qualifier where Thierry Henry's infamous handball helped dump the Irish out and send France through.
Asked if he felt any sympathy for the Estonians, Keane told reporters: "No-one felt sorry for us two years ago."
Ireland's defence will face something of a reshuffle as full-back Stephen Kelly will miss the game with a groin injury. He is likely to be replaced by Sunderland's John O'Shea, who returns from a hamstring strain.
