The England international is out of contract at Arsenal at the end of the season, and negotiations have so far failed to reach an agreement between the two parties, leading to speculation Walcott could leave the club, with Manchester City reportedly interested.
Walcott is free to begin talks with other clubs when the January transfer window opens, as he will have just six months left on his Gunners contract.
And City's new sporting director Txiki Begiristain is keen to bring Walcott to the club. The report claims City are willing to make an offer to Arsenal, if the north London club want to recoup a fee for the 23-year-old, but they are also prepared to wait until the end of the season in an attempt to sign him for free.
In the past three seasons, the Premier League champions have convinced a number of Arsenal's first-team players to move to the Etihad Stadium, including Samir Nasri, Gael Clichy and Emmanuel Adebayor.
They reportedly attempted to persuade former-Arsenal club captain Robin Van Persie to sign for the club, only for the Dutchman to join rivals Manchester United in a £24m deal last August.
The report claims City are desperate to sign a winger, with Tottenham wide-man Aaron Lennon their first target. But Roberto Mancini's side are now reportedly set to turn to Walcott, who wants £100,000-a-week to stay at the Emirates Stadium.
The Daily Star also reports that Walcott is a target for Chelsea, Liverpool and Manchester United.