The Lions are understandably keen to bring the striker on board full-time, with the New Zealand international in rich goalscoring form during a three-month loan stint at The Den.
West Brom are prepared to discuss a deal, with Wood some way down their attacking pecking order, but they are aware that a bidding war could be sparked in January.
Millwall claim they are being messed around in their attempts to put a transfer in place before the window opens, and say their latest bid can be considered a 'take-it-or-leave-it' offer by the Baggies.
"They told us £500,000 and I said fine. They said £1million and I said fine. So I've gone for it already - I'm done. That's it," Lions chairman John Berylson told newsatden.co.uk.
"For us, it's a take-it-or-leave-it offer. We're not going to increase it but I'm sure West Brom are thinking about an auction.
"If we take our bid off the table, which is worth well over £1million - that's not including a sell-on clause either - and West Brom end up selling him for half that in the future, they will look stupid. That's the biggest danger really, looking stupid.
"I know Huddersfield are in there but Chris has a flat in London."
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