The Donegal middleweight is now 12-0 in his professional boxing career after a knockout win against the Puerto Rican in California earlier this month.
The win was on the undercard to Bernard Hopkins and Joe Smith Jr's fight.
"I'm in this sport to become multiple world champion and make as much money as I can," Quigley told the BBC.
"Beating him (Melendez) in the style and fashion that I did puts me higher up those rankings and gets me that one step closer to the world title shot.
"The way the fight panned out I made it very easy for myself and that's exactly what you do, you don't get paid for overtime in boxing."
Melendez came into the bout with a 28-8-1 record, with 26 KOs.
But the former amateur world silver medallist stopped his opponent in the first round and made short work of what was scheduled to be a 10-round bout.
The next 12 months are expected to be a breakthrough year for the man whose career is being steered by Oscar De La Hoya's Golden Boy Promotions.
"Billy Joe Saunders, Canelo, Golovkin, Danny Jacobs... these are the boys that I need to beat, so these are the boys I have my eyes on," Quigley said.
"For me, my next fight is going to be the end of February, start of March. So 2017 is going to be a massive year for team Quigley.
"I just keep my head down and keep working hard because I want to keep climbing that ladder and getting those belts."
Ireland's Jason Quigley has said he wants to fight the "biggest names" in boxing after an impressive victory against Jorge Melendez.