The 22-year-old was subject to a last minute £92m bid by Arsenal on transfer deadline day in the summer.
The France global is reported to have made Liverpool his preferred choice, but excited Arsenal fans earlier this week when he liked a post on Instagram suggesting he was set to sign for the Gunners.
Monaco's Thomas Lemar celebrates after scoring a goal during the Ligue 1 match against Saint-Etienne. The interest in him hasn't dropped down though, with the Gunners among those still in the player's pursuit.
And, as per an update from Ladbrokes today, the Blues have now moved ahead of Liverpool into 2nd-place in the list of favourites to land Lemar, with the Premier League champions having seen their odds slashed to just 2/1.
However, Arsene Wenger may have to look elsewhere as he aims for a top four finish.
The same report also claims that Chelsea remain "keen" on tying up a deal to sign Monaco forward Lemar, who was heavily linked with a move to Arsenal in the summer months. The Merseyside club's interest in him perhaps stems from Barcelona's unrelenting chase of Philippe Coutinho, who hasn't quashed exit rumours either.
Barcelona still want Coutinho but since they also plan to sign Griezmann through his £100m release clause, they have become reticent about the type of fee that purchasing the Brazilian would require, with Liverpool so far insisting that even an offer of £120m would not convince them to sell. He moved to Monaco in the summer of 2015 for an offer of €4 million ($4.75 million).