Mt. Gox filed for bankruptcy after discovering it had lost bitcoins belonging to customers and itself.
Deploying Nasdaq's software could give Noble greater legitimacy.
"It is a vote of confidence in bitcoin the technology," Nicholas Colas, chief market strategist at Convergex Group, said in an interview.
"Now that you are seeing big organizations providing technology, there's a feeling that bitcoin is here to stay."
While some bitcoin start-ups have recently built their own trading technology, Nasdaq's system has been battle-tested for years.
Nasdaq provides trading software to companies including Japan Exchange Group Inc. and Singapore Exchange Ltd., which are among the biggest market operators in the world.
"Nasdaq is open to providing its technology to other bitcoin exchanges," Ryan Wells, a Nasdaq spokesman, said during an interview.
Noble was founded by John Betts, whose resume features stints at Goldman Sachs, Morgan Stanley and UBS Group.
Betts said his finance career included designing trading systems.
His time working for the giants of finance may be a sign of maturation for bitcoin, and contrasts with Mt. Gox, which was originally envisioned as a place to buy and sell playing cards for the game Magic: The Gathering.
Nasdaq's involvement is a good sign, according to Adam Draper, a venture capitalist at Boost VC who invests in bitcoin start-ups.
It "obviously shows that they think bitcoin is here to stay," he wrote in an e-mail, referring to Nasdaq.
