The forward has completely fallen out of favor at the Stamford Bridge club under boss Enzo Maresca.
The no.10 is not first choice, with the likes of Nicolas Jackson and Cole Palmer preferred to him.
Chelsea paid RB Leipzig £52 million to bring in the 27-year-old in 2023, with Nkunku scoring 15 in 41 games, largely as a substitute.
Asked if he could be sold or loaned out recently, coach Maresca replied: “Not at all. I spoke with Christo days ago - he did not say he is not happy.”
Maresca added: “The problem with Christo, not the problem but the same issue we have mentioned many times; if you play with Cole (Palmer), Joao (Felix), Christo, Jadon (Sancho) or Noni (Madueke) - who is defending? Their skill is not defending. The last game, we tried with Joao and Cole together.
“Probably the best moment for Christo with us has been in pre-season, playing in his position. Since we started, he is playing as a nine for us. Against City, he played as a winger; knowing this is not his best position. His best position is as a 10 but Cole is playing there. We need balance.”