Jose Mourinho's appointment as Real coach earlier in the summer prompted speculation the Spanish giants would launch a bid for Gerrard.
Former Chelsea manager Mourinho tried to sign Gerrard during his time in charge at Stamford Bridge, but appears unlikely to make a renewed effort to work with the England midfielder.
Gerrard's future at Anfield had been the source of debate following the club's failure to qualify for the Champions League next season and the departure of Rafa Benitez.
However, Bronzetti has revealed that Real president Florentino Perez is not keen to add Gerrard to his squad for next season, with a hefty price tag one reason behind the reluctance to make a bid.
"Kaka will stay at Real, but the president does not agree with Gerrard because he is 30 and Perez doesn't want to know," Bronzetti told GR Parlamento.
"Plus, Liverpool asked for 70million euros [£58million]."
Bronzetti revealed Mourinho is keen to sign a player in the mould of Gerrard after ruling out an offer for Inter Milan full-back Maicon.
He added: "Mourinho is convinced to leave Sergio Ramos on the right and now he wants a central defender or midfielder like Gerrard.
"Real did not make an offer for Maicon, there was a request of 35m euros £29million] from Inter."