The Mexican defends his WBC super-bantamweight title against Jesus Ruiz this Saturday in Las Vegas, but is hoping to battle some fellow belt holders in the near future.
Quigg, the current WBA champion, has voiced his desire to face Santa Cruz, but is expected to be sidelined until the summer after undergoing hand surgery.
A fight against IBF king Frampton also interests the California-based boxer and he will wait to see if the Belfast man makes a successful first defence against Chris Avalos in February.
Asked about a clash with Frampton, Santa Cruz told Sports: ???Yeah, I think so, I want to fight him.
???I???ve been wanting to fight him since a while ago. He has the IBF now so I think a unification could come right there.
???Right now, I think he???s got a mandatory against Avalos, so hopefully after that one – if I???m available – I would like to unify against him.???
Quigg made three defences of his title last year and was pursuing a major fight in America before injuring his hand.
Discussing the Bury man, Santa Cruz said: ???His trainer and his manager have been telling me that he wants to fight me and I???ve been telling them that I want to fight him too.
???But right now he has a hand injury. If I???m available when he???s better, then I???m willing to fight him too.???
The prospect of travelling to Europe has not been dismissed by Santa Cruz, who has only previously fought in America or Mexico.
???I would like to fight over there because they say it???s really nice. I???m willing to go and I???d like to go to different places to fight.???