Gatland backed up a Six Nations Grand Slam during his first year at the helm in 2008 by steering Wales towards their first World Cup semi-final since 1987.
The New Zealander has won rave reviews as a result, and Wales skills coach Jenkins said: "I think he is one of the best, if not the best coach in the world.
"He is up there with (All Blacks) coach Graham (Henry) as far as I am concerned.
"Other than last year, the seasons we've had under 'Gats' have been pretty impressive.
"First up, the Grand Slam (2008), and then the second year we were only fractions away from back-to-back Grand Slams - it was about one pass in Paris, and then a kick at home against Ireland."
Gatland is under contract with the Welsh Rugby Union until after the 2015 World Cup in England, and Jenkins added: "We have got to try our best to keep hold of him.
"I know (WRU chief executive) Roger Lewis and people at the union would love him to stay. We all want him to stay, and I think it is important we try to keep Warren.
"We have a very young and talented side, and there is a bright future ahead for Wales."
Gatland has been linked repeatedly with succeeding New Zealand boss Henry when the All Blacks supremo steps down after the World Cup, but Lewis said last week that Gatland's new WRU deal is "watertight".
Wales, beaten 9-8 by France in the World Cup semi-final two days ago, must now turn their attention to Friday's bronze medal match against Australia.
"It's a Test match at the end of the day, and it is a chance to become the third best side in the world," Jenkins said.
"We would have loved to be in the final playing against the All Blacks. It wasn't to be, but this is an important game for us on Friday, one we've got to get up for and one we have got to perform in.
"The guys have had an excellent tournament so far, and we certainly don't want to let ourselves down on Friday.
"The two games we've lost here we have lost by a point both times. We know we are a very good side and we feel we have made an awful lot of progress throughout the tournament.
"We want to show sides what we are about and we want to turn up on Friday with another big performance.
"In a funny way, you would much prefer to be in the third/fourth game than not be involved at all and already be at home, although the final is the one we all want to be in."
Jenkins, meanwhile, has backed Wales captain Sam Warburton to make a quick recovery from the crushing blow of his World Cup being ended by suspension.
Warburton has started serving a three-week ban following his sending off by Irish referee Alain Rolland for a dangerous tackle on France wing Vincent Clerc in the semi-final.
Prop Gethin Jenkins is favourite to assume leadership duties when Wales face the Wallabies at Eden Park, with Dan Lydiate possibly being switched from blindside to openside as Warburton's replacement.
"What's gone is gone, there is not an awful lot we can do about it," Jenkins added, following Warburton's red card and subsequent disciplinary hearing.
"We have obviously got to respect the decisions they have made and move forward. We will move on and take the medicine that has been given to us.
"To be fair to the young kid (Warburton), he has been outstanding. He has been outstanding all tournament in terms of his play and his leadership.
"Sometimes, in disappointment you learn a lot about yourself. He is not a malicious player, we all know that, he's a fantastic player.
"It is something you have just got to get over and recover quickly from. I am sure he will recover quite quickly from it."
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