The Moroccan playmaker is on loan with the Rossoneri for the remainder of the season after his spell with Fulham was cut short.
Taarabt made an immediate impact for Milan with a brilliant individual goal in the weekend's 3-1 loss to Napoli and is now hoping he can become a less temporary fixture at the San Siro.
"It's a dream to be at AC Milan and it was fantastic to score on my debut. I hope it's the beginning of a great adventure," he told the Milan Channel.
"I don't know why I wasn't playing at Fulham. I'm now at Milan where there are so many important players and I'm happy to be here.
"I still have four months to prove that I can play in this team because I want to stay at AC Milan."
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