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 will not be involved in the FA Cup fourth round tie at Brentford on Saturday, Rodgers said there is an outside chance he could feature in Tuesday's League Cup semi-final second leg against Aston Villa.
"He's not available for the weekend and there will be a question mark for Tuesday, although it's certainly not as serious as we first thought," Rodgers told reporters on Friday.
"It's not his hamstring, it's a glute, so we're hopeful for Tuesday, but there's a little bit of work to do. He'll get some work in with the medical team. He'll stay with them for the weekend.
"He's much better than directly after the game, when he was tight and sore and struggling to move. But today he was much better."
Meanwhile, Leicester midfielder Nampalys Mendy was also injured in the first half against West Ham with a knee problem and Rodgers said he will be out for up to six weeks.