Since Chelsea missed out on Jules Kounde to Barcelona last month, they have been credited with a strong interest in Leicester's 21-year-old central defender.
Fofana made just seven Premier League appearances for the Foxes last campaign after suffering a fibula fracture, but impressed when playing 28 league games as Leicester finished the previous season in fifth.
It has been suggested Chelsea could break the world-record fee for a defender – currently the £80million paid by Manchester United for Harry Maguire – with a move for Fofana, as reports claim the Blues have already seen two offers knocked back.
And Rodgers insisted no satisfactory offer has been tabled as he claimed another season at the King Power Stadium would benefit Fofana.
"There were two [bids], but nowhere near what the club would consider," Rodgers told a news conference on Thursday.
"We're not looking to sell. Naturally if there's interest from other clubs, that is looked at by the club. He's a top young defender and there are not too many around his age.
"Another year for him at least [at Leicester] would be really important for his development. Wesley is quite calm on the situation. He is aware of the interest. He's just getting on with his work.
"It can affect the whole group if you don't manage it. You have to keep your eye on the ball. But everyone is focused on doing their best in games for Leicester City."
Fofana started as part of a three-man defence as Leicester began their Premier League campaign with a 2-2 draw against Brentford last Sunday.
Meanwhile, Leicester have allowed long-serving goalkeeper Kasper Schmeichel to join Nice and remain the only Premier League side without a senior addition in the transfer window.
And Rodgers concedes the club must sell to buy as they look to rebalance their squad, telling the BBC's Kammy and Ben's Proper Football Podcast: "Now the expectation is so high that eighth doesn't seem where we should be.
"We will continue to push but we don't have the resources. This season will be a season for us where we try to balance the books.
"Most big teams, you can see they go out and are able to spend big again. We haven't been able to do that, we are trying to balance our books.
"My concentration is on the players we have. Players are developing and improving and then we'll see how far up the table we get. We'll not set any targets now but we'll enjoy the journey and see where it takes us."