The ex-Argentina international was sacked by Spurs on Tuesday night after a difficult start to the Premier League season for the north London side.
Pochettino’s dismissal still came as a surprise given that he had led Tottenham to their first-ever Champions League final last season.
The former Espanyol boss had also led Tottenham to a top-four finish in the last four seasons, something which Arsenal haven’t been able to emulate.
Current Arsenal manager Unai Emery is under pressure at The Emirates following their below-par start to the top-flight campaign.
The Gunners are in sixth place in the Premier League table following a run of one win in their last six games.
Emery’s handling of the Granit Xhaka fall-out as well as his tactical decisions during games have led to criticism of the Spanish head coach.
Former Arsenal defender Keown believes the Gunners should show ambition by making an approach for Pochettino.
“There’s no need to panic at Arsenal, we are getting close to panic by the way, because we’re not having the best of seasons, but the powers that be at the top of the club should be seriously considering Pochettino,” Keown told the Daily Mail.
“I have a lot of admiration for what he did at Tottenham, the way he nurtured those young players and he didn’t spend a great deal of money.
“I don’t think Tottenham spent enough.”
Arsenal appointed Emery as Arsene Wenger’s replacement in May 2018 after previous stints in charge of Paris Saint-Germain, Spartak Moscow, Sevilla and Valencia.
The Gunners finished in fifth place in Emery’s first full season in charge.
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