Guus Hiddink is currently in charge at Stamford Bridge following his appointment as Jose Mourinho's successor, but the Dutchman is only in west London on an interim basis and will leave at the end of the season.
Per the Times' Rory Smith, Pochettino is a key target for the Blues to replace Hiddink, along with Diego Simeone, Jorge Sampaoli and Didier Deschamps.
Pochettino has impressed in the Premier League since moving from Espanyol to Southampton in 2013.
His season-and-a-half at Spurs has seen the north London side improve noticeably, and they currently lie fourth in the English top flight, five points clear of fifth-placed Manchester United.
Their recent excellent run of form has put them firmly in contention to qualify for Champions League football next season, and moved them into the top 10 of Bleacher Report's European club rankings:
The eye-catching performances that Pochettino has managed to draw from his young English players—Harry Kane, Dele Alli, Tom Carroll and Eric Dier—has undoubtedly attracted the attention of Chelsea also.
Given the immense youth talent the Blues have at their disposal—they have won the FA Youth Cup in three of the last four seasons—the Argentine would seem like a good fit at Chelsea, especially if owner Roman Abramovich wants a manager who will build a legacy at the club.
However, Pochettino's current attachment to Tottenham could prove a sticking point, as there is little love lost between the two London outfits, and the 43-year-old still has more than three years left on his contract at White Hart Lane.
He has terrific pedigree having won La Liga with Atleti and got them to a Champions League final, and it would be exciting to see how he would fare when backed by Abramovich's money.
Sampaoli, who recently resigned as Chile boss, would be more of a risk as he has never managed at club level in Europe.
However, his record with Chile was outstanding, as he turned them into one of the world's best sides with an admirable 2014 World Cup campaign followed by a 2015 Copa America triumph, per Opta:
61% - Jorge #Sampaoli won 61.4% of the games and guided #Chile to win their 1st Copa America in history. Farewell https://t.co/NAKK8lmjdH2016-1-19 19:55:03
Deschamps—the only non-Argentine on the list—is currently in charge of the French national side, but he could potentially be persuaded away after the summer's European Championship.
He would undoubtedly be a popular appointment given his playing history at Chelsea, but he seems to be the least likely of the four to be appointed.