The 20-year-old is the top scorer in Belgium's Pro League with 18 goals, with his form seeing him linked with a number of high-profile clubs in the January transfer window, including Everton.
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"There is a good philosophy at that club [Arsenal] and there is confidence in young players in a technically strong team that cares about football. I've loved the club from childhood," he told Belgian television show 'La Tribune'.
"I am a person with vision, I want [to move] ahead as quickly as possible. I'm going to make a decision in consultation with my agents and my family but, at this moment, I have signed nothing."
Batshuayi also revealed that he has already rejected the chance to join Anderlecht, feeling that it was not the right move for his career.
"I was pleasantly surprised by the interest of Anderlecht, which made me an offer," he added. "It's a big team in Belgium but, for me, it was better this season to stay at Standard."