The veteran striker has been out since the final game of 2021 with an injury but is back in training and could be involved for the March 1 trip to Burnley.
Rodgers felt his side were almost back to their best in an unfortunate 2-1 defeat at Wolves on Sunday and hopes the return of key players will help them.
Jonny Evans, Wesley Fofana, Justin James and Timothy Castagne are also currently injured.
“Jamie’s probably seven to 10 days away from rejoining the squad,” Rodgers said following the Wolves game.
“Jonny is still a number of weeks, Wesley is training but we need to manage him back. Timothy is a few weeks away. JJ will be in the next week or so.”
Rodgers also explained that Harvey Barnes, who missed the loss at Molineux, should return for the Europa Conference League clash with Randers in the week.
“He was due to play but felt a bit of stiffness in there,” Rodgers said. “It was too much of a risk really. With a few days to rest, he should be back for Thursday.”
Wolves have no such issues as a sixth win from their last eight Premier League games have seen them force their way into Champions League qualification contention.
Ruben Neves got them started against Leicester with an early strike from outside the box and after Ademola Lookman levelled for the Foxes, Daniel Podence earned the three points.
“We are working a lot during the week to get the three points on a matchday,” Neves told the club’s official website.
“We will not do a lot different from now on, just keep working, game by game, trying to get maximum points. It’s our way to work, to do it.
“It was a really hard game for us. Leicester played well and we were a bit short to press them because they have a lot of quality – we knew that before the game. I think our mentality brought us the three points.
“When you need to win like this, even if you don’t play like you used to play, it’s really good.
“It was a fantastic win for us, a massive three points and we just want to keep it going. We needed to defend more than normal. Leicester went to our box a lot of times. Our strength was key to the win.”