The last thing Arsenal supporters would want after witnessing a comprehensive win over their most bitter rivals is news that could dampen their spirits, yet that is what has come to pass after Arsène Wenger revealed after this match that even if Theo Walcott has not signed a new contract with the club by the end of the year he will not be sold in January, thus creating the possibility of the forward leaving Arsenal for nothing next summer.

Walcott's current deal expires on 30 June and he has still not agreed to an extension, with the player refusing to commit to a five-year contract worth £75,000 a week and holding out for one that would see him earn £100,000 a week.

Wenger has stated his desire for the stand-off to be resolved "one way or the other" before Christmas, leading to the assumption that should Walcott not have committed to Arsenal by then he would be sold during the next transfer window, with Liverpool consistently linked with the 23-year-old.

But, asked after Arsenal's 5-2 win over Tottenham – during which Walcott assisted Per Mertesacker's opening goal for the hosts before scoring their final one himself – if the England international would be sold in January if an agreement had not been reached by then, Wenger said he would not. Then, asked if that meant Walcott would be staying until the end of the season, the Frenchman said he would.

It was a firm stance from the Arsenal manager but this is a situation that can quickly slip from his control given Walcott would be free to speak with overseas clubs in regards to signing a pre-contract agreement on a Bosman transfer if he is not tied down to a new deal in the next two months. And if that did not occur, he could join whoever he wished for free in July.

Walcott's departure would not leave Arsenal fans in despair – he is no Patrick Vieira, Thierry Henry, Cesc Fábregas or Robin van Persie – but it would still frustrate them to see no financial return on a player they paid Southampton an initial £5m for in 2006 and who is now worth double that, and be deemed as another example of the club's cack-handed approach to managing their better players.

"I hope Theo signs [a new contract]," said Jack Wilshere. "We know what Theo brings; he's got pace, he can go behind, and his movement and timing is probably the best around. He can play anywhere up front but wants to play down the middle, and I think he will get his chance. He just has to be patient."

In that regard, Walcott did not do himself many favours against Spurs. He was a constant threat from the right wing, with his cross for Mertesacker's 24th-minute header expertly executed. Walcott also played a key role in Santi Cazorla's strike on 60 minutes that made it 4-1 to Arsenal, but prior to scoring his ninth goal of the season the player twice failed with good opportunities to test Hugo Lloris in the Spurs goal. Little wonder, then, that Wenger again questioned his ability to be Arsenal's principal striker.

"You have situations where the goalkeeper kicks the ball out and [Olivier] Giroud flicks the ball on or controls it on his chest – things Theo is not capable of doing," he said. "He is a different type of player."

Emmanuel Adebayor used to be Wenger's leading attacker and it was perhaps no surprise that he played such a pivotal role in this derby, scoring the game's first goal on 10 minutes before being sent off for a reckless lunge on Cazorla seven minutes later. The visitors were always going to struggle thereafter and having seen Mertesacker equalise, conceded twice more before the break, through Lukas Podolski and Giroud. Gareth Bale's 71st-minute strike made it 4-2 but ultimately Walcott would have the final word, cementing relief and joy for a club that, by its manager's admission, had been suffering from a crisis of confidence. It is now Tottenham, with three successive league defeats to their name and Adebayor suspended for three games, who find themselves in troubled times.

Man of the match: Santi Cazorla (Arsenal)