The Blues, fresh off their 4-1 victory over Tottenham last Monday, face Manchester City in the Premier League on Sunday.
Spurs saw two players handed long-term injuries in that match, with James Maddison and Micky van de Ven ruled out until the New Year.
But Pochettino gave Chelsea fans a positive update on the current situation surrounding both Nkunku and Lavia, although the game against Pep Guardiola's side will come too soon.
"We had some conversation and he [Cristopher Nkunku] said to me I want to be ready for after international break, Newcastle," Pochettino told reporters previewing their Sunday showdown.
"I asked him yesterday and he said hmmm, and I said you are liar.
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"It is close and he is really well. We are happy with him."
The 51-year-old Argentinian tactician also provided an update on Lavia's fitness.
Chelsea beat Liverpool to the midfielder in a £58m deal from Southampton in August.
The 19-year-old is yet to feature for the Blues, though, but could soon be handed his debut for the club.
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"Romeo Lavia is also close. He trained today on the pitch. Hopefully with the team next week," Pochettino added.
Chelsea have not beaten Guardiola's side since their 1-0 Champions League final triumph back in 2021.
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After playing City in both the FA Cup and the Carabao Cup last season, the Blues have failed to win their last six meetings with them.