The Colombian had been linked with the likes of Juventus and Barcelona with his current deal set to expire in June 2014.
However, Zuniga is set to put pen to paper on a new deal that will see him earn €3.5m (£2.9m) a season, plus bonuses - with the contract reported to have a €30m (£25.1m) release clause inserted into the contract.
The 27-year-old, who can play as a full-back or a wing-back, joined the Azzurri in 2009 from Siena for €9m (£7.5m).
The deal is set to make Zuniga the second highest paid player at the club behind Gonzalo Higuain.
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