The defender has been linked with a move to Russia, but is keen to stay put and help the San Siro side secure a Champions League spot
The Italy international was being heavily linked with a move to Zenit St Petersburg, but says he is keen to stay at Milan and help the club qualify for the Champions League after a difficult start to the 2012-13 campaign.
"Leaving Milan? [Adriano] Galliani received an offer for me, but he told me that the club want me to stay put. I have always worked hard for this club and behaved professional and will continue to do so," Abate told reporters.
"Reaching third place [in Serie A] will depend on the matches against our direct rivals. It's only normal that you will have to win those games if you want to qualify for the Champions League."
The defender then went on to praise Stephan El Shaarawy, who has been struggling in recent weeks, and stressed that the youngster can still be a game-changer for Milan in the remainder of the season.
"El Shaarawy can be decisive between now and the end of the season. He carried the team for a long time, and is now paying for that a bit."
Milan currently sit fifth in the Serie A table with 41 points from 24 games.