The Italian defender was rumoured to be close to signing for Zenit St Petersburg in the January transfer window but he insists that his loyalty was always with Milan.
Abate told Corrie Dello Sport: "The transfer market? There was a concrete offer, not just rumours. I spoke with [Milan vice-president] Adriano Galliani and he wanted me to stay. Milan is my priority.
"I started badly with an ankle injury in the Berlusconi Trophy and then a pulled muscle. After the Christmas break, I got back in shape and things have gone well since then."
Milan are currently third in Serie A.