But Jones believes the international schedule is already hectic enough.
"I don't think we need another tournament to take away from the Tests we play annually. We've already got a World Cup," Jones told The Courier Mail.
The former Wallabies coach conceded Millar's aim to put more emphasis on Test rugby is the correct thing to do, but the chairman is going about it the wrong way and that a 'mini-World Cup' is simply not the answer.
Millar intimated he believed a tournament that included South Africa, Australia and New Zealand, along with the powers from the northern hemisphere, should be held two years after every World Cup.
Millar believes the proposed tournament, coupled with end-of-season tours being cut down, would have plenty of benefits.
"It would solve many things such as concern over player welfare and number of matches," he said.
"It would create more relevant games and be a more effective way of increasing revenue."
Jones was asked about the issue as he flew out to Whangarei with the Queensland Reds for their first pre-season practice match against the Auckland Blues on Wednesday.
Boom recruit Clinton Schifcofske will start the match in full-back as Queensland attempt to plug the gap left by Chris Latham, who suffered a serious knee injury recently.
The 2007 Rugby Union World Cup kicks off in September.