Jones denied that he had already been approached by the Japan Rugby Football Union (JRFU) for the national coach's job.
"If Japan came to me, I'd be very, very pleased as it's a great honour.''
He said he would "definitely'' take the national team job if all conditions are met, including "Suntory's blessing.''
Jones said Kirwan, 46, "definitely improved'' both the team and a number of players.
He said what Japan lacked the most was the "consistency of their application of skills.'' He added their "decision-making positions'' needed to be improved.
Japan will host the World Cup in 2019 and will be looking to avoid the embarrassment of becoming the first host country to fail to make the knockout stages.
JRFU vice president Nobby Mashimo told AFP that no specific name had been raised as a candidate to replace Kirwan, a hero of New Zealand's triumph in the inaugural 1987 World Cup on home turf.
On Saturday, the Top League, the country's premier rugby union division, will start its season, which was shortened due to the World Cup and will end in late February.
"I think it would be great if we can make a decision (on the new coach) by the year-end,'' he said.
The JRFU is scheduled to hold a board meeting on Saturday to review the Brave Blossoms' coaching structure.
- NEWSTALK ZB