Zaniolo has emerged as a top target for Aston Villa and the club are pushing to take the Italian to the Midlands in the ongoing transfer window.
Their previous offer, which consisted of a €5m loan fee and €25m option to buy, was rejected by the Turkish giants.
Aston Villa director of football Monchi wants the player and Villa have decided to increase the offer worth up to €32m.
They have upped the option to buy figure by €2m, but according to Turkish broadcaster A Spor, Galatasaray are still not keen to accept the bid.
The Turkish giants are still cool on the latest offer despite Zaniolo being open to moving to Villa Park this summer.
Galatasaray want a mandatory purchase clause rather than an option to buy as part of the deal that could be worth up to €35m.
It remains to be seen whether Aston Villa are ready to meet Galatasaray’s expectations to get the deal over the line.
Zaniolo is claimed to be waiting to see the outcome of the talks.