Conte has followed up his title-winning season with a dismal second campaign in which Chelsea finished outside of the Champions League places.
The Italian has also fallen out with Chelseas hierarchy on several occasions over the clubs transfer policy, as well as the handling of players within the squad.
According to The Sun, Abramovich has already identified Pochettino as Contes successor and the Spurs manager is aware of the interest.
Pochettino is also set for talks with Spurs chairman Daniel Levy over the clubs direction this summer.
The Tottenham manager is understood to be willing to offload Mousa Dembele, Danny Rose and Toby Alderweireld and wants to improve his squad with a £150 million transfer budget.
Pochettino also wants his key players, namely Harry Kane and Christian Eriksen, to be offered new contracts.
Conte, meanwhile, publicly insisted after Chelseas 3-0 defeat to Newcastle United on the final day of the Premier League season that he is ready to honour his contract, which still has a year left to run.
For me, this is important, not speculation around me. Its not important. The most important thing is what the club thinks, not you or the speculation about me, he said.
I have a contract and the club know very well the situation. After Saturday, we go on vacation and then we will see next season.
More: Chelsea FC