American Gatlin dominated last year's Diamond League, running 9.77 seconds and 19.68 secs in the 100m and 200m.
Coach Glen Mills said Bolt had stepped up his preparations since running 46.37 seconds over 400m in Kingston in March.
"Usain's made significant strides since the last time you saw him," he said.
Gatlin, 33, won 100m Olympic gold in 2004 and World Championship gold in 2005.
"We take all competitors with a level of seriousness," added Mills. "But the truth of the matter is Usain at his best doesn't have much to worry about."
Bolt, 28, ran only three races last year. He is next due to run in a 100m race at an athletics meet in Rio on 19 April, and will follow that by representing Jamaica in the World Relay Championships in Bahamas on 2 and 3 May.
"I want to run really fast this season so I'm working on it," he said.
"I'm happy with where I'm at. I'm doing a lot of work leading up to this first run in Brazil [in April] - that's the focus and that's what we're working towards."
Bolt will bid for a third 100m gold and a fourth 200m gold in succession at August's World Championships in Beijing.
Multiple Olympic champion Usain Bolt has made "significant strides" as he bids to defend his world titles this season, and is unconcerned about the challenge of sprinter Justin Gatlin.