Walcott, the Gunners' top scorer with 11 goals this season, is out of contract at the end of the season and will be free to talk to other clubs over a summer move if a new deal is not agreed by January 1.
As exclusively revealed by Goal.com Premier League side Chelsea have been tracking the England international for some time now and have made the attacker one of their top targets to replace Liverpool-bound forward Daniel Sturridge.
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The 63-year-old was speaking ahead of his side's home clash with Newcastle on Saturday, with the north Londoners 10 points, and eight places, better off than the Magpies.
However the Frenchman insisted that Alan Pardew's side, who were only denied a point against league leaders Manchester United after a last-minute Javier Hernandez winner on Boxing Day, will provide a stern test and said his team must win the game.
"At Old Trafford at times they made Manchester United look vulnerable defensively," he told reporters. "They could have won.
"Last year's game [against Newcastle] was vital and this season's is similar. We can't drop points."