The tickets remaining are mainly in the extensions to the Centenary stand upper and lower tiers.
Ticket prices start from £32 for adults and £18 for under-16s and OAPs, while Junior Hammer prices start from £16.
Ticket office manager Steve Kitcher says: "After Saturday's excellent win over Manchester United the increase in demand has been huge.
"The tickets that are remaining are mainly in the extensions to the Centenary stand and these areas were only recently confirmed as ready for occupation - hence us still having tickets available.
"The capacity versus Arsenal will be 34,500 as we are still awaiting the release of the new seats in the Bobby Moore stand.
"It now looks as if we will have to wait until the new year for a bigger capacity crowd."
As for the FA Cup third round tie against Macclesfield on Sunday, January 6th at 1pm, there is no possibility of the game being played at Upton Park, as some reports have suggested.
"The only thing that has changed is the day of the game, but not the venue," says Steve.
There will be an allocation of 1,500 terrace tickets priced at £10 for adults and £6 for under-16s and OAPs, and 400 seats at £14 for adults and £9 for under-16s and OAPs.
If applying for tickets using a postal application please note that the small number of seats received will be sufficient for bondholders and away match credit scheme holders, but it is not expected that any seats will remain for sales to season ticket holders.
Bondholders can apply on Thursday, 13th December, and season ticket holders on Saturday, 15th December.
Should any tickets remain they will be sold to club members from Wednesday, 19th December.
Fans buying tickets in person should be aware that the ticket office has now relocated back to the west side of the stadium.
Supporters should enter via the main gate in Green Street and turn left at the Dr Martens stand reception.
For telephone bookings please phone the booking office on 020 8548 2700.