The Bantams are now just one game away from a historic triumph and a place in Europe next season, and the 35-year-old admits the prospect is "too unbelievable for words"
Victory over the Swans would cap a remarkable run that has seen the Bantams become the lowest ranked team since Rochdale in 1962 to make the final of competition.
And success in the final would also see Bradford play in the Europa League next season, for the first time in their history - something Jones freely admits he never thought would happen.
“I was watching the Europa League and it was Liverpool playing in Russia,” he told the Daily Mail.
“I sat there thinking, ‘That could be us next season!’ Just imagine playing Inter Milan on the Thursday and Dagenham on the Sunday. It’s too unbelievable for words, but that shows you what we have achieved.
“Everyone connected with Bradford City should enjoy this moment. We’re all dreaming. Seeing all that claret and amber at Wembley is going to be amazing.”
It’s been a long journey for the 35-year-old, who started his career as a winger playing for Welsh club Caernarfon Town before moving to Sunday’s opponents Swansea.
“Caernarfon was a good grounding, but the standard wasn’t the best,” Jones added.
“I must have done something right, though, because Swansea spotted me and Jan Molby signed me up.”
The Englishman still fondly recalls his time at the Vetch Field, the Swans old stomping ground, and is delighted to see the lightning progress his former club have made in recent years.
“It was many, many moons ago, but I do remember the Vetch was a bit of a fortress," he continued. "The ground was really old-fashioned and there was a prison next door. Not many teams liked going there.
“Swansea have come on in leaps and bounds. They weren’t that far off going out of the League at one stage, but now look at them.
"It’s nice to see, because it’s a lovely city with very passionate supporters. It mirrors Bradford really.”