Sterling, who played the full 90 minutes in the 2-0 loss at the hands of Tottenham on Sunday, has only scored once in 2023 after netting in the 1-1 draw with Nottingham Forest.
The former Man City star has made only 15 starts out of a possible 24 for the club this season owing to a poor run of form and minor injuries. But he is still regarded as a key player by Graham Potter and on reported wages of £300,000-a-week, he is one of the club's highest earners.
His current deal expires in 2027 and it would take a huge amount for Chelsea to even consider selling him to Arsenal, even after the arrivals of forwards Mykhaylo Mudryk, Noni Madueke and Joao Felix in January.