The Welsh region, formed in 2003, find themselves tenth in the GUINNESS PRO12 table having claimed just three wins from 13 games this term.
Yet by stark contrast their form in European competition has been exceptional, with three wins from four ahead of Saturday's trip to Newcastle Falcons leaving them on the verge of progressing to the next stage.
And Jones, former head coach of Russia, believes it's time to finally find the keys to the Rodney Parade trophy cabinet.
"Ten years ago, I managed to win this tournament as part of the Sale coaching staff and it was a great achievement, something I'm proud of," he said.
"For the Dragons to get a trophy would be great. The first step is the next two weeks. Then anything can happen in quarter-finals.
"I made it to the semi-final of the Heineken Cup as a player with Gloucester and the quarter-finals with Sale and the pool stages are always the hardest part.
"If we can get out into a quarter, who knows, we have every chance of getting into the final and making it a big season for everybody."
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