Vardy was forced off during the first half of Wednesday's Premier League win against West Ham after initially trying to continue playing after he suffered the injury.
Vardy has scored 17 goals for Leicester this term, making him a key figure in the team's unexpected surge into the top four.
It was feared the 33-year-old could be sidelined for several weeks in a blow to third-placed Leicester's hopes of securing a spot in next season's Champions League.
But while Vardy wasn't involved in the FA Cup fourth round tie at Brentford, Rodgers said there is an outside chance he could feature in Tuesday's League Cup semi-final second leg against Aston Villa.