Pennant's current loan runs out on December 19th, but The Gunners have already stated that they are willing to let him stay on at Leeds.
The 20-year-old will sign for another month and it's hoped that will become a rolling arrangement which will see the player stay until the end of the season.
Gray said in the Yorkshire Evening Post: "It's something we're working on and hopefully we can get everything sorted out early next week. Jermaine has done well for us and I would be delighted if we could keep him."
Birmingham City are known to be interested in signing Pennant on a permanent basis.
However, the player is happy to remain at Elland Road and it's unlikely Arsenal will consider any deal before the end of the season.