"I don't want to go anywhere," the center told The Athletic. "I love my teammates. I have a family, you take that into account."
The 34-year-old is under contract through the end of the 2021-22 season and has a no-trade clause, TSN reported, but shows no inclination to waive it.
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"If we are going into a rebuild, I'm going to do my best to teach the kids how to be a pro and how to win," he said.
The Ducks (19-19-9) had some success earlier this season. They were 19-11-5 after winning 11 of 13 games from Nov. 21-Dec. 17 and were three points behind the first-place Calgary Flames in the Pacific Division.
Anaheim has not won since. It has struggled offensively in large part because of an injury to forward Corey Perry, who tore an MCL during warmups before a preseason game Sept. 24 and has not played this season.
Perry is one of a host of Ducks players who have missed significant time, along with forwards Patrick Eaves (29 games, broken rib) and Rickard Rakell (13 games, ankle), defenseman Cam Fowler (23 games, facial fractures) and goalie Ryan Miller (14 games, knee). Kesler was also sent back to Anaheim to be re-evaluated for a lower-body injury, sustained in the second period of a 3-1 loss to the Detroit Red Wings on Tuesday, and is out for the remainder of a five-game road trip that ends at the New York Islanders on Sunday.
The frustration has taken its toll, particularly on center Ryan Getzlaf, who has three points (one goal, two assists) in his past 11 games and 32 points (10 goals, 22 assists) in 41 games this season.
"Hardest thing I've been through in my career by far," the Anaheim captain told the Orange County Register. "Been through some tough years, but this one, having a stretch like this, I've never been through. It's been really tough. I can give you every cliche in the book with the way things are going now."
The Ducks are not planning to fire coach Randy Carlyle, who is their all-time leader in wins (382), general manager Bob Murray said Jan. 13. Carlyle won the Stanley Cup during his first stint with the Ducks in 2007 and has guided them to the Stanley Cup Playoffs in seven of his eight full seasons as coach.
"I'm more focused on our players," Murray said, "specifically with who is going to step up in this situation. … We have higher expectations for this group and they should expect more from themselves."
Anaheim has made two trades this week, acquiring forward Devin Shore from the Dallas Stars for forward Andrew Cogliano on Monday, and acquiring forward Justin Kloos from the Minnesota Wild for forward Pontus Aberg on Wednesday.
