Quigg has successfully defended his world title on three occasions after picking up the vacant belt last year, but the Lancashire fighter has admitted that he is keen to secure a showdown with WBC titlist Santa Cruz.
The 25-year-old told IFL.TV: "I'm hoping to get the fight with Santa Cruz. He's mentioned my name and said that he wants to fight me.
"I don't think that there is a bigger fight in the super-bantamweight division, aside from the Carl Frampton fight, than me and Santa Cruz. Those are the fights I want.
"We have been in talks with their team for about a month now, and hopefully that fight happens."
If a deal can be agreed for the match to take place, likely to be in the United States, both men would be putting their unbeaten records on the line.