Goals from Marcos Alonso, Eden Hazard and Cesc Fabregas now mean the Gunners are 12 points adrift of the Blues at the top of the table.
It also came just days after a humiliating 2-1 defeat to Watford at the Emirates.
But Shearer believes Arsenal will keep Wenger due to his work behind the scenes rather than on the pitch.
Arsene Wenger's future at Arsenal is in doubt
Arsenal player ratings against Chelsea
Sat, February 4, 2017
Express Sport brings you Arsenal's player ratings from their 3-1 defeat to Chelsea
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"The question that’s being raised over and over by fans is: Should Wenger go?" he told The Sun.
"All I’d say is if I was a businessman and owner and had Wenger in charge of my operations, I would be quite happy to sit tight.
"The ground is full every week, so say the figures.
"He has overseen a move from the old Highbury to the new Emirates which has set the club up for life.
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Arsenal were thumped 3-1 by Chelsea on Saturday
"He makes sure the money keeps rolling in by finishing top-four and getting in the Champions League, even if they keep going out early in the knockout stages.
"He doesn’t spend wildly. His net outlay over the last four transfer windows is just £10million more than United spent on Paul Pogba.
"They’re regularly on TV because they can be pleasing on the eye.
Alan Shearer believes Arsene Wenger will stay at Arsenal
"And hey, they finished second last season as well, lest we forget.
"So for those in the boardroom, what is there not to like?
"Business-wise Arsenal know that under Wenger things will tick over very nicely, thank you.
"More and more football is ruled by men with calculators rather than those with the tactics board."