Talks between Lucic's agent and Kings GM Dean Lombardi have picked up, but as Lucic told the Times, there is "nothing to get excited about" just yet.
"There's been two or three little talks here and there," Lucic told the paper. "My plan is to remain a King and hopefully finish off my career here. Like I said, I go day by day and you never know what tomorrow is going to bring.
"If I could look eight, nine, 10 years down the road, hopefully I play that long. I hope it is right here in L.A. and that something can get done and conversations can get picked up in the near future because I really have enjoyed my time this season and love being a King and living here in L.A.
"Hopefully, it can last more than one season."
The Kings, meanwhile, are also looking to add at least one other major piece to their roster prior to the Feb. 29 trade deadline.
Lombardi and his staff have expressed interest in Winnipeg Jets captain Andrew Ladd and defenseman Dustin Byfuglien, as well as New York Rangers blueliner Keith Yandle, among others.