The England international could be sold before the transfer window on Friday for a fee believed to be in the region of £12 million.
Arsenal have a choice to make, sell him now for a profit or risk losing him on a free transfer next summer.
Champions City are pondering a move, along with Liverpool, after talks broke down to sign Swansea City's Scott Sinclair. The speedy winger was on the bench for Sunday's 0-0 draw at Stoke.
However, Walcott is thought to have demanded nearly £100k weekly but Arsenal feel their offer of £75k is a good raise from his £60,000-a-week salary.
Arsenal may not be reluctant to sell the wideman as they have enough reinforcements in young 18-year-old Alex-Oxlade Chamberlian while Gervinho got the nod for the clash against Stoke.
But it is unlikely that Walcott will sign for City, with the depth in their squad, the winger would have to settle with lesser playing time. But Liverpool can be a good move for Walcott with more first-team chances.
Arsenal have already lost captain Robin van Persie to Manchester United, Alex Song to Barcelona and in the meantime, outcast striker Niklas Bendtner is holding talks with AC Milan.