According to James Olley, Theo Walcott has put contract negotiations with Arsenal on hold until the offseason, meaning we're likely to have a repeat of Theo Walcott's last contract negotiation with Arsenal. Supposedly both sides are "relaxed" about the situation, which I suppose explains why Arsene Wenger was making jokes about it last week.
The first contacts have been established with the embassy. We will see how that progresses politically. He is very quick on the pitch but off the pitch, not always.
There are also reports surfacing from multiple sources that Liverpool is interested in Walcott if he doesn't re-up with Arsenal, in part because evidently Raheem Sterling is making them sweat out his own contract situation and they see Walcott as a possible replacement.
I would imagine that the most likely scenario here is that the two sides wait until summer, negotiate for a while, and then if a deal doesn't come together Walcott will probably be sold. I would personally prefer to keep him, but Walcott isn't quite the key man that he was in 2013 when he signed this deal. If he's asking for an amount that doesn't make sense, he can be replaced from within, by Alex Oxlade-Chamberlain or Danny Welbeck, or by a new player.
Arsenal are in a much better negotiating position now than they were two years ago. It's likely they will use that to their advantage. This could go on for a while.