Walcott has not made a single Premier League appearance for Arsenal since the start of October, with his last three outings occurring in the EFL Cup and Europa League.
The 28-year-old will see his current deal at the Emirates Stadium expire at the end of the 2018-19 campaign, and his future has been the subject of much speculation.
Everton, West Ham United and Southampton have all been credited with an interest in a player that has lost his spot in the England squad after struggling for regular club football.
According to The Times, Walcott is not prepared to discuss a new contract with Arsenal until next summer as he waits to see whether his Premier League involvement increases in the second half of the season.
Walcott has scored 108 goals in 392 appearances for Arsenal since a 2006 move from Southampton.