Both outfits were linked with the Argentine sharpshooter with rumours swirling that Madrid tactician Jose Mourinho was prepared to offload Higuain.
However, father Jorge, who also serves as his son's agent, revealed in an interview on Saturday with La Stampa that the player would stay put at Real as long as the club are happy for him to stay.
"At Real Madrid nobody has been talking about wanting to sell Gonzalo, and he also does not have any intention of leaving. In fact the idea is to continue the relationship until his contract expires in June 2016," he explained.
"If someone told us that we are no longer welcome [at Madrid], I am sure that the offers would not be bad," he continued.
While heralding both Chelsea and Juventus as "two great clubs", Jorge added that "in any case they would be two huge opportunities, but no-one has talked to me."
Higuain has netted an impressive 12 La Liga goals in just 15 matches for Madrid this season so far.