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The 19-year-old's loan spell ends on January 1st but Simpson is more than happy to extend it, if a deal could be struck between the two clubs.
"The manager has mentioned to me about extending my loan if Arsenal agree, and I would love that," said Simpson. "I eventually want to go back to Arsenal and fight for a place there, but right now I am playing for Millwall and I want to do as well as I can here.
"When I first came I felt like an outsider, but now I feel part of the team.
"I haven't been thinking about going back, I have been thinking about playing for Millwall and getting the right results."