The reigning Premier League champions have been linked with a move for the Leicester City ace and Ladbrokes make it just a 6/4 shot a deal gets done before the transfer window slams shut.
That means he’s far more likely to move to Stamford Bridge than former targets Sergio Aguero (8/1) and Pierre-Emerick Aubameyang (10/1).
Ladbrokes spokesman Alex Apati said: “This one really has come out of nowhere, but with Chelsea in desperate need of some added firepower up top, we’re taking no chances.”
Vardy has recovered from a foot injury and is fit to travel for Leicester’s Carabao Cup clash with Sheffield United tonight.
Vardy was subbed in the closing stages of last Saturday’s 2-0 win over Brighton.
But boss Craig Shakespeare said the 30-year-old trained yesterday and will feature against the Championship side.
“Jamie trained this morning okay,” Shakespeare told the club’s website on Monday (www.lcfc.com).
“He was a bit sore yesterday, but he was okay to train today.
“He is okay and will be involved tomorrow. At what length, we will have to wait and see. I plan to make changes.”
Shakespeare also said midfielder Nampalys Mendy, who sustained an ankle injury in March, could play at Bramall Lane.
Defenders Robert Huth (ankle) and Wes Morgan (back), midfielders Danny Drinkwater (thigh)and Vicente Iborra (groin) and forward Kelechi Iheanacho (toe) have been ruled out of Tuesday’s match as they recover from their respective injuries.