The London Evening Standard says the dip in form and the Spanish international's wage demands have made them uncertain about keeping him.
Costa, 28, has scored just three goals in 2017 and was a target for Chinese Super League club Tianjin Quanjian in January.
Now Costa also wants an increase on his £150,000-a-week wages at Stamford Bridge.
Club chiefs are unsure whether Costa is worth the money and know Tianjin are offering an eye-watering £650,000-a-week to the hitman.
Former club Atletico Madrid are also interested in Costa and the striker has hinted he is not entirely happy with life in London.
Costa revealed after the Cherries win:“I am happy at Chelsea, I am not necessarily saying that I am happy with my life in London. But that is something totally different."