Trapattoni is sweating over the fitness of his first choice keeper after the 36-year-old was unable to take part in a session on Saturday morning due to blisters
The 36-year-old returned to team training at Giovanni Trapattoni's preparation camp in Italy on Thursday following a knee injury, and was again reduced to the sidelines on Saturday due to blisters.
When asked if the keeper was struggling, the Italian told reporters: "Yes, a little bit, but it was better also to let him have a rest because he has worked too much, and it is better that he is fresh, and also mentally fresh."
The Aston Villa keeper had gone to London to see a specialist about the knee problem earlier in the week, before admitting he had doubts about making the tournament.
The Republic face a trip to Hungary on Monday in their last warm-up game before travelling to the Euros. Given is now a doubt for the fixture despite his manager indicating that the keeper would play to prove his fitness.
Trapattoni will be hoping that his number one recovers in time for the competition, with Ireland already facing a tough task in Group C where they will face Italy, Spain and Croatia.
He added: "It is true that we have a possibility to call another [player], but it would be better if we finished this friendly game without a problem."