The 23-year-old right winger has been the subject of widespread speculation linking him to top Premier League clubs, as contract negotiations with the Gunners reportedly stalled.
"It is all speculation," said an Arsenal spokesman, according to ESPN. "Negotiations are ongoing. Arsene Wenger and Theo Walcott had a heart-to-heart talk on Wednesday and both parties are committed to proceeding with a new contract.
"The player will not be sold before the end of the transfer deadline."
Wenger recently stated that Walcott was "very important" to Arsenal's future.
However, numerous sources suggest he will exit the Emirates. Walcott is valued at £15 million, and he has prominent suitors.
According to The Times, Walcott rejected a contract from Arsenal this week, and remains a target of Manchester City and Liverpool.
City are heavily engaged in transfer talks before the Aug. 31 deadline, and are expected to make multiple deals. Arsenal are reportedly monitoring striker Edin Dzeko, so the two sides could be negotiating a deal that would move Walcott to the Etihad and Dzeko to the Emirates.
In July, The Sun reported that Liverpool boss Brendan Rodgers was looking to add Walcott, and Metro reported that the Reds were pursuing him on Aug. 12.
Chelsea appear to be out of the running for Walcott. Daily Star reported on Aug. 14 that the Blues had joined Inter Milan in pursuit of Walcott, but there have not been any recent reports of either club actively targeting him, and Chelsea appear to have their sights set on a striker.
Arsenal may feel that Walcott is expendable due to the development of star winger Alex Oxlade-Chamberlain and the addition of Santi Cazorla, who is also capable of operating from the right side. Walcott has been a rather inconsistent performer with the Gunners, and Wenger may not be able to receive a higher transfer fee for a player with his contract expiring next summer.
Walcott has 42 goals in 222 appearances with the Gunners, and has 28 appearances and four goals with England. He joined Arsenal in January 2006 from Southampton.