Captain Wes Morgan will be offered a new contract by Leicester.
The skipper's deal runs out at the end of the season and new boss Brendan Rodgers has told the Foxes board he wants him to stay.
Morgan, who led the club to their shock 2016 title win, has played 21 times this term including starting Rodgers' first game, a 2-1 defeat at Watford on Sunday.
Rodgers said: "I've spoken to the club and I would like him to get a year. He is ready if needed and of course he understands the position he is in – that he won't start every game. It happens to the best.
"As long as he can respect and understand where he is in the team and what the role is I would love to have him here.
"He has made clear he would love to be a part of this. Hopefully between now and the end of the season we'll resolve something.
"He will have a part to play, even if it's not starting. He is at that stage, and it comes to them all but the thing with Wes is he still makes a valuable contribution to us."
Morgan, 35, joined Leicester from Nottingham Forest in 2012 and has made 292 appearances, scoring 12 times.
Fellow title winners Shinji Okazaki, Danny Simpson and Christian Fuchs are also out of contract with their futures yet to be decided and Rodgers knows their situations need to be handled respectfully.
"There needs to be a bridge for them, absolutely. I understand that. That's communication, that is just seeing where they're at," he added.
"Some guys will want to stay, some will want to play. We'll assess that over the next couple of months. There is no one more than me who will respect that, from looking from the outside at what they achieved.
"What they've given not just to this club, but to football. The story was absolutely amazing. I've found them really, really good guys. We have to protect their pride while also looking to improve in the summer."
Mid-table Leicester host struggling Fulham in the Premier League on Saturday, with Jamie Vardy on 99 goals for the club.
The former England international has netted 10 times this term and Rodgers is eager for him to add to his tally.
"His story is amazing and I'm so happy he's here, I've always wanted that striker at the top end to press, that's so important for my teams," Rodgers said.
"He's had two chances since I've been here and scored two goals. It's our job to create more chances for him.
"When I went to Liverpool they'd scored 47 goals and within two years they were the first Liverpool team to score over 100 goals.
"Hopefully in time I can do the same here and create a really dynamic team."
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