Gatland's money is on Ireland
The Irish will be bidding for a hat-trick of Six Nations titles under Kiwi coach Joe Schmidt, although they will be without some key players including retired former skipper Paul O'Connell.
Wales begin the championship against Ireland in Dublin on February 7 and Gatland, who named his squad on Tuesday, believes a side coached by fellow New Zealander Schmidt will still be tough to beat.
"I think one of the things about the Irish is that they would like to go in with people writing them off, even though they have won the championship for the last two years," said Gatland, himself a former Ireland coach.
"They have to go in as favourites. The thing about any Irish team is that you write them off, and you do that at your peril."
He added: "We go into this tournament respecting them immensely, and particularly what they have achieved under Joe Schmidt over the last two seasons.
"I think they are favourites for the tournament, given the experience they have at knowing how to win, particularly under pressure. They have lost a couple of experienced players, but it is going to be a tough proposition for us."
Both England (Eddie Jones) and France (Guy Noves) have new coaches and Gatland said: "The Six Nations is a little bit of an unknown quantity, I suppose, in terms of a couple of new coaches with France and England."
Meanwhile Gatland was delighted by the decision of experienced lock Alun Wyn Jones to sign a new national dual contract with the Welsh Rugby Union and the Ospreys.
"The service he [Jones] has given to Welsh rugby has been fantastic.
"It's been a pleasure for us to see him develop as a player into an extremely valuable and experienced member of the squad. He's world-class, and the fact he has committed himself to Welsh rugby is fantastic, both for the Ospreys and for us.
"The ideal scenario is we want all our players, if possible, playing in Wales.
"It means we have the ability to train with them, and to look after them from a strength and conditioning and a medical point of view. Having them here makes the regions stronger, and it helps the national team as well.
"We are under a lot of pressure, obviously, from English and French clubs in terms of the salaries that have been offered to players, and that's something we are going to have to deal with going forward.
"The goal is to try and keep as many players as we can playing in Wales."
Agence France-Presse
