The Argentine is into his second season at Spurs, and appears to be building a special team, with a heavy focus on young players.
He would be the ideal candidate for a side like Chelsea, who have found previous managers to be reluctant to integrate their many talented young players, with more than 30 currently out on loan across Europe.
The Times report Chelsea expect strong opposition from Spurs chairman Daniel Levy, and have three other candidates on their shortlist, including Diego Simeone, Jorge Sampaoli, and Didier Deschamps.
The Independent claim former Juventus manager Antonio Conte is also among their options.
The only hope for Chelsea regarding Pochettino is that the Argentine walked away from Southampton two years ago for the Spurs job, which may give them belief they can tempt him away with a better offer.
Yet Pochettino has everything he needs at Spurs to be successful, and could even end this season as a league winner, a current impossibility for Chelsea.