The 18-year-old played at left wing-back on Sunday after Ben Chilwell and Marc Cucurella were both ruled out for the remainder of the season.
Starting away at Manchester City after facing Nottingham Forest last week, Hall was bright in the defeat at the Etihad Stadium and showed his ability by keeping Riyad Mahrez quiet.
A much-changed City side proved too strong for Chelsea, who gave the champions a guard of honour before kick-off.
But the Blues battled well and Conor Gallagher hit the post with a header from a whipped cross from Hall. The teenager had two good efforts himself and finished the match having created the most chances for his team and with the most touches in the opposition box.
Pochettino wants to build his Chelsea squad around a core of homegrown players and, wherever he was watching the game on television, the Argentine would have been impressed by Hall.
Though he played on the left on Sunday, Hall is primarily a powerful central midfielder who has shown a goal threat at youth level with his consistent ball-striking ability.
He has played all but one of his nine first-team matches this season out of position and his versatility will appeal to Pochettino.
So will his temperament, having been thrown in at the deep end in four matches against City this season, as well as away games at Liverpool, Newcastle and Fulham.
Unlike his teenage City counterpart Rico Lewis, Hall has been forced to handle his breakthrough from the academy in chaotic circumstances.
He did not play for almost four months after Chelsea took their spending this season to over £600million in January and found himself in limbo, splitting his training time between the first-team and Under-21 squads and often playing at centre-back in the youth team.
Amid their struggles this season, Chelsea seemingly forgot about Hall, despite the fact he has hardly put a foot wrong.
He has only two years left on his contract and there is a feeling that young English players could be sold this summer to help the club stay in line with Financial Fair Play [FFP] rules. Selling homegrown stars would count as pure profit under the new version of UEFA's FFP regulations, allowing Chelsea to more easily balance the books.
But Pochettino will be intrigued to take a close look at Hall. He turned talented young players like Harry Kane, Dele Alli, Kyle Walker and Danny Rose into England regulars at Tottenham and it would be no surprise to see Hall ahead of Cucurella as back-up to Chilwell next season.
Interim manager Frank Lampard described Hall on Sunday as a “quiet lad” who “definitely needs to come out of himself a little bit more”, but said: “In terms of quality, if you see him with the ball and the things he can do, he has got the levels.”
Given what he has shown this season, Hall at least deserves the chance that Mason Mount, Reece James and Trevoh Chalobah were given before him.