The London Evening Standard says two unnamed players chose not to move to Stamford Bridge due to concerns over Conte's long-term future.
While there was no official word from Chelsea, doubts over the Italian's future were a major factor in them deciding not to join the Blues.
After defeat at West Ham, Conte again declared they needed to buy in January.
He said: “I can give my opinion to my club and also I speak with my club. I can give my opinion but the final decision is for the club. It is right to be in this way."