The 73-year-old Italian made the admission after assessing Monday's 0-0 draw with a youthful Hungary side that failed to qualify for the tournament. It would be a huge concession as it would be the first time he has been willing to alter it since taking charge in 2008.
Ireland's central midfield pairing have been found wanting when facing a three-man midfield, and despite acknowledging the problem in the past, Trapattoni was reluctant to change his formation.
"I know this problem with lineup," he said. "I have to speak with them about this sacrifice, it's important. We have to speak about it, we have to make this consideration with the team. When we played against Russia [in the qualifying campaign], Alan Dzagoev gave us a difficult time, so we...must consider the opportunity.
"In 1977, we [Juventus] won the UEFA Cup and one of our best defenders was our striker. We spent the last 15 minutes in our box, but we won."
Ireland's squad were put through their paces for almost an hour in training, although goalkeeper Shay Given, defender John O'Shea and midfielder Glenn Whelan took no part, with Trapattoni later insisting they were rested, rather than injured.
The trio will return to training on Wednesday, having complained of 'heavy legs' after playing in the rain-soaked Ferenc Puskas stadium on Monday. Earlier, winger Aiden McGeady had complained about tiredness among some members of the squad due to Trap's punishing training regime, but the Italian rejected the claim, insisting that it was in the Spartak Moscow player's mind.
"I do not think they were tired," Trapattoni said, with a smile, "psychologically maybe they were, but not physically. It's not true we make hard training, in this moment the players don't need training, they need rest. It was only a light training session."
Having seen Ireland's Group C opponents holders Spain, Croatia and Italy also struggle in their Euro warm-up games, the Ireland coach said the pressure of competing at a major tournament was impossible to escape.
"The players are beginning to think about the stress of the competition, it is as much a psychological commitment as a physical commitment," said Trapattoni, who guided Italy to the 2002 World Cup finals and the Euro 2004 finals.
"Spain struggled against China [a late winner giving them a 1-0 victory], but we know that in the competition, the first game is always the most important and leading up to that always creates tension."
Ireland have enjoyed a relatively serene buildup to their opening game on Sunday against Croatia, with a 1-0 victory over Bosnia in Dublin, an easy win against a Tuscan select XI during their training camp in northern Italy, and Monday's scoreless draw.
Unlike Spain, Italy and Croatia, they have avoided injuries to key players - the one thing Trapattoni has wished for ahead of the tournament. The coach also expressed his shock at the warm welcome Ireland received at their EURO 2012 training base where almost 13,000 Polish well-wishers cheered his squad at the Municipal Stadium. Ireland landed in Gdansk at 2am (0000GMT), having flown from Budapest.
The team met the mayor in the morning and trained at the home of club Arka Gdynia in the early evening, but there were thousands of fans there beforehand, taking advantage of a party atmosphere that included face painting and a Titanic-styled bouncy castle.
"It was a great surprise," admitted Trapattoni. "I heard that maybe 1-2000 would come, but it was fantastic. I think we have to pay our respects back for this kindness we received today."