Captain Sam Warburton and fellow Wales forward Alun Wyn Jones have been sidelined by injuries while Dan Biggar is having an ankle injury assessed.
But Gatland is not worried about any of his players with the 10-match tour starting on Saturday, 3 June.
"We've pretty much got a clean bill of health," he said.
"There are no concerns with anyone in the squad at the moment.
"With the modern game everyone is carrying knocks from week to week and we're pretty pleased where everyone in the squad is at the moment."
Fly-half Biggar, 27, is to have tests on an injured ankle after limping off in Ospreys' 40-17 defeat by Scarlets in the Pro12 on Saturday.
Cardiff Blues flanker Warburton sustained a knee injury in April, ruling him out for six weeks but could play for his region before the end of the season.
Ospreys lock Jones has been out for seven weeks after injuring his shoulder playing for Wales in their 20-18 Six Nations defeat by France in Paris in March.
Ireland scrum-half Conor Murray made his comeback from a shoulder injury in Munster's 50-14 Pro12 win over Connacht.
British and Irish Lions head coach Warren Gatland says he currently has no injury concerns before this summer's tour to New Zealand.