They are now expected to return ahead of Chelsea's trip to Newcastle on Saturday, with both Nkunku and Lavia having potentially four more training sessions to prove their fitness to Mauricio Pochettino's staff.
Neither Nkunku nor Lavia have made their competitive Chelsea debuts yet, with both players suffering injuries shortly after their arrival.
Pochettino has bemoaned the loss of Nkunku in recent weeks, a £52million summer signing from RB Leipzig, who he built his attack around in pre-season.
The 25-year-old scored three goals during the US tour before his untimely knee injury in the final match on tour in the United States.
Reece James, Raheem Sterling, Marc Cucurella, Armando Broja, Benoit Badiashile and Robert Sanchez have also trained this week alongside a host of youth players who have not joined up with national teams.
James opted against joining up with Gareth Southgate's squad to further his recovery from a recurring hamstring problem. He said over the weekend: “I haven’t felt this good in a long time. I definitely feel my strength and fitness building up again. Recently, I’ve been able to play consistently.”
Pochettino and his non-international players have been given several days off, with James visiting Rugby World Cup-winning South Africa captain Siya Kolisi in France.