However, with Walcott's place at Arsenal now more unclear than ever before, rumours have emerged over the last couple of days that West Ham are ready to reignite their chase of the experienced wide-man upon the opening of the winter transfer window in January.
Everton have lacked tempo and dynamism in the final third so far this term following the sale of Romelu Lukaku to Manchester United over the summer, despite spending over £140 million on reinforcements themselves. Koeman left with the Toffees in the bottom three and had ironically spent most of the summer trying to sign another Arsenal striker, France global Olivier Giroud.
Asked if he would keep the Englishman in January, however, Wenger said: "Yes".
Arsene Wenger refuses to put international football ahead of Arsenal, will stick to rotation policy
Walcott has failed to start a single Premier League game for the Gunners this season, making just three substitute appearances in the league, with the majority of his game time coming in the Europa League.
The Gunners expect to lose Alexis Sanchez and Mesut Ozil next year, and will need to sign replacements.
The likes of Everton and Southampton have been linked with January moves for the 28-year-old but Wenger is adamant that he does have a future at Emirates Stadium. Now, with the addition of Lacazette, it seems as if Walcott's time in North London is coming towards an end.
Arsenal have enough depth in attacking areas to let Walcott go and try and make the grade elsewhere, even if it means selling him to a rival.More news: US ITC finds Canada lumber harms US producers, duties to remain
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