The Gunners are hopeful of reaching an agreement, having been in advanced talks since before Christmas.
The arrival of right-back Fox, 25, would pave the way for the departure of Switzerland international Noelle Maritz.
Maritz, 28, is poised to join Aston Villa, although an agreement has not yet been fully reached.
Villa would need to pay a small fee with six months remaining on Maritz's contract at Arsenal and there is also interest from a few clubs in the WSL.
However, Villa are Maritz's preferred destination and they are very hopeful of signing her this January.
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