The 31-year-old Los Angeles Galaxy striker is due to arrive in Dublin from the United States on Monday after undergoing a scan on a hamstring strain.
Trapattoni said: "The news is the scan in the US was not bad. We are not worried and we await him with confidence."
The news came as the bulk of the remaining members of Trapattoni's squad met the 10 who joined up last Thursday to start training in Malahide.
Defender John O'Shea, who is nursing an ankle injury, worked only in the gym, while Keith Fahey and Kevin Foley, who have groin and hamstring problems respectively, trained apart from the group.
Trapattoni is confident all three will be able to work with the rest of their team-mates before the squad flies out to Italy next Sunday for a pre-tournament training camp.