talkSPORT understands the Blues expect to bring in the ex-Tottenham manager as a permanent replacement for Graham Potter.
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The Argentinian has emerged as the frontrunner to take over from caretaker boss Frank Lampard after Julian Nagelsmann withdrew from the race.
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Pochettino is well known for his time with Spurs, helping the club reach the Champions League final in 2019, only to lose out to Liverpool.
However, it was their semi-final victory over Ajax in Europe's elite competition that brought the 51-year-old to tears.
Lucas Moura's second-half hat-trick secured a dramatic 3-2 win over the Dutch side, ensuring Tottenham made history by progressing to their first ever Champions League final.
"It is difficult to talk. I am so emotional," he said. "Thank you football. My players are heroes.
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"The second half was amazing. This type of emotion is impossible without football.
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"It is an amazing moment and it is difficult to explain in words."
Moving to Chelsea could soon have Spurs fans reduced to tears, especially if he turns the Blues' fortunes around.
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Pochettino is still hugely popular in north London but working for Tottenham's arch-rivals could change that.
"I'm going to be gutted if we let Poch go to Chelsea when we're in desperate need of a manager," one fan wrote on Twitter. "Feels like a betrayal from him too after all his talk of loyalty to his clubs and how they were arguably as big of a rivalry as Arsenal during his tenure."
Another said: "If Poch goes to Chelsea we gotta just move on, he will never come back at least not as a homecoming. It will always be the ex Chelsea boss trend that we seem to love in recent years. Gutted but that's that now."
A third posted: "I would be absolutely gutted if Poch went to Chelsea, but I wouldn't blame him at all. He's out of work and Spurs haven't approached him. My anger would be firmly aimed at Levy and his inability to read the room."
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"It seems that a fairytale return is not going to happen and that Poch will be the next Chelsea manager," a fourth said. "Absolutely gutted and it will hurt to see him do well there but he owes our board nothing. If they didn't come knocking he has every right to seek employment elsewhere."