The person spoke Wednesday on condition of anonymity because an agreement had not yet been completed. The deal is pending the 40-year-old Colon passing a physical.
New York was in the market for a starter after ace Matt Harvey had elbow reconstruction surgery, which will sideline him for next season.
General manager Sandy Alderson had said he didn't want to give a long-term deal to a pitcher because New York had several prospects close to being ready.
Colon went 18-6 with a 2.65 ERA for the Oakland Athletics in a season in which he began by completing a 50-game suspension for a positive testosterone test.
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