With Diego Costa's future at Stamford Bridge still uncertain, the Blues are considering their options, and Vardy is believed to be on the list, according to The Mirror.
The England international was pivotal in Leicester's shock title win in the 2015-16 campaign, scoring 24 goals and becoming the first player to net in 11 consecutive Premier League fixtures.
Last season, the 30-year-old took time to get off the mark, but he ended up netting 13 times, and two games into this campaign he has already scored twice.
The report adds that Chelsea are close to securing a £30m deal for Vardy's teammate Danny Drinkwater. body check tags ::