Jonny Evans could sign a new deal with Leicester before the end of the year.
The Northern Ireland defender's current contract expires in the summer but talks over a fresh two-year offer are at an advanced stage.
Boss Brendan Rodgers said: "I'm hearing from the club it's pretty close. We're very hopeful very soon we'll be able to finalise that agreement.
"It could be sooner than that (January), we'll just wait and see.
"I know the representatives of Jonny and the club are very close.
"If it's this year, great, if it's the New Year, hopefully it'll be very early."
Evans' deal will bring an end to speculation he could return to Manchester United.
The 32-year-old came through the Old Trafford ranks as a schoolboy and spent a decade at the club before joining West Brom in 2015.
He made 131 Premier League appearances for United and lifted three Premier League titles and two League Cups.
Ulsterman Rodgers had always been confident he would sign a new deal.
Evans joined from West Brom for £3.5m in 2018 and has played 87 times for the Foxes, scoring twice. He returned from suspension to help Leicester beat Tottenham 2-0 on Sunday and lift them to second in the table.
Evans' imminent new deal is further good news with the club due to move to their new £100m training ground this week.
The first team will train at the facility, which has a private nine-hole golf course, for the first time on Christmas Eve.
Rodgers added: "The players have an amazing recreational area, they can sit outside and have their tea and coffee. There are rooms for them so when they train in the morning they can have their lunch and then have a sleep and train in the afternoon. There are analysis hubs where they can analyse their game."