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16 March 2019, 09:38 | Updated: 16 March 2019, 09:40
Head coach Gatland's Wales Six Nations adventure started in triumphant fashion 11 years ago when his players were crowned unbeaten champions.
It was Wales' second clean sweep in four seasons following a Mike Ruddock-inspired success in 2005, while they repeated the feat under Gatland four years later.
If Wales beat Ireland in Cardiff on Saturday, they will claim another title and Grand Slam in Gatland's final Six Nations game at the helm.
It would also be a Five or Six Nations record for any coach, and provide Wales with a dream send-off into this year's World Cup, which will be Gatland's swansong before he steps down.
"He has a bit left on his contract, so we won't let him get too far ahead," Wales captain Jones said.
"But he came in with one (Grand Slam), and it would be nice for him to leave with one.
"There is a big 80 minutes before we can look at the romantic and sentimental side of it.
"It's his last Six Nations, but there is a bit to go yet, so we are not going to let him sail off into the sunset just yet."
A Wales win - they have claimed 13 successive Test victories since Ireland toppled them at the midway point of last season's Six Nations - would see Jones join an exclusive club.
It would be his third Six Nations Grand Slam, which is a feat achieved by just three other Wales players - Gethin Jenkins, Adam Jones and Ryan Jones.
"There are a lot of different people to the ones that have been involved before," Jones added.
"I've said before, the closer you get to something like this, the further away you can be sometimes.
"We are very grounded, we know we have to work hard. In every performance we've had, there have been areas for improvement.
"You want to put yourself in this position. Ask any rugby player - this is what you dream about.
"We are at home, with what is going to be a great atmosphere, and these are the occasions you work for."
Ireland can still win the title, but they must beat Wales and hope that Scotland claim a first Twickenham victory over England for 36 years.
"Domestically, you look at the success the Irish teams have had over the years," Jones said.
"In the last 18 months, as well, they've probably set the standard in northern hemisphere international rugby.
"They've claimed a few big scalps and they have been, arguably, the most consistent team. We are well aware of their calibre."
The Principality Stadium roof, meanwhile, will be open for Saturday's game, Press Association Sport understands.
Despite a weather forecast for Cardiff on Saturday of strong winds and torrential rain, Ireland have requested that the roof remain open.
Wales' preference is for it to be closed, but both teams must agree, or - under Six Nations regulations - it stays open.
Wales trained with the roof closed at their traditional eve-of-game captain's run on Friday.
Asked about the roof situation, Jones said: "We know, as players, that it's going to be open.
"You would have to ask the Irish guys about what their mentality is.
"We've trained here on a few occasions with it open and closed. At the end of the day, the pitch and conditions are the same for both teams."