Sanchez, 28, came close to joining City during the summer transfer window, but the move broke down on deadline day.
Arsenal will begin talks with 18-year-old Eddie Nketiah over a new contract after his Carabao Cup heroics against Norwich City last week.
The Citizens have been in brilliant form this season, winning nine of the 10 games thus far, while drawing the other.
Nketiah proved his worth coming on as a second half substitute, scoring two goals against Norwich City to lead the north London club to the fifth round of the Carabao Cup.
Manchester City were expected to move for Alexis Sanchez in the January transfer window. However, they will now look to sign the Arsenal forward on a free transfer in the summer.
Arsenal left-back Sead Kolasinac suffered a recurrence of a hip injury during the Gunners' 2-1 victory over Swansea City on Saturday (28 October).
Sead Kolasinac and Aaron Ramsey both score as Arsenal recover from a first-half deficit to beat Paul Clement's Swansea at the Emirates Stadium.
The Gunners last won the title in 2003-04 when they went the entire season unbeaten but recent years have seen the competition pass Wenger by.
Arsene Wenger has previously admitted Arsenal could sell Sanchez in January, instead of losing him for free in the summer.
Stuttgart midfielder Berkay Ozcan has claimed that Arsenal have been closely following him for the last two years.
Walcott has seen just 47 minutes of Premier League action this season and is far down the pecking order in north London.
Manchester United, Arsenal and Bayern Munich have approached Jose Arnaiz's agent to sound out his contract situation at Barcelona.
Swansea City will be without four players for the Premier League trip to Arsenal with Wilfried Bony and Renato Sanches still out with muscle injuries.
Nketiah, 18, spared the Gunners' blushes by coming of the bench to net a brace in their 2-1 Carabao Cup victory over Norwich in midweek.
Carabao Cup quarter-final draw eventually has to be pre-recorded after a technical delay lasting almost two hours.
Arsenal CEO Ivan Gazidis fielded questions on transfer policy during the club's latest AGM on Thursday.
Ronald Koeman failed to sign an adequate replacement for Romelu Lukaku, who left Everton to join Manchester United in the summer.
The fans were up in arms over the decision to extend Arsene Wenger's contract but Stan Kroenke decided to persist with him, saying the easy call would have been to sack the Frenchman.
Arsenal majority owner Stan Kroenke has no plans to sell the club having rejected a £1bn offer from Alisher Usmanov earlier this year.
Round Five of the Carabao Cup draw will be held at Twitter's UK hub in central London at 4pm BST on 26 October, Thursday.
Stan Kroenke remains hopeful that Arsenal can re-sign contract rebels Mesut Ozil and Alexis Sanchez to new deals before the end of the season.
Mesut Ozil will reportedly only leave Arsenal for three clubs – Manchester United, Real Madrid and Barcelona. The German is not interested in moving to Italy or Turkey.