The 17-year-old Ghanaian was spotted playing for local side Woodford United last year, after moving to Britain just over 12 months ago.
He is now starring for Birmingham's Development Squad, but his performances are reported to have attracted interest from rival clubs.
Birmingham boss Lee Clark has confirmed that talks are ongoing with Arthur and they hope to tie him down to a long-term deal.
"We are quite a way down the line in terms of a contract for Koby," Clark confirmed to the Birmingham Mail.
"We are waiting to hear back from his agent about the proposals put to him.
"Although you can never be sure, we are confident that things will be done and dusted in the next few days."
Clark is really happy with how Arthur, who has been handed a squad number but is yet to make his league debut, is progressing.
"Koby is coming more and more into my thoughts," admitted Clark.
"He was outstanding on Monday against Coventry and he has really done well in the development games and training.
"You never know what opportunities might come, if he carries on like this.
"Certainly, he will be in and around it for our next match, at Crystal Palace."