Per The Athletic's Matt Barrows, Jack Bechta, Kittle's agent, said he is prepared to be "very patient" getting a new contract for the 26-year-old.
"He's the poster child of culture for that team, of the type of player they want on that team," Bechta said.
Kittle is entering the final season of his rookie contract with a $2.144 million base salary in 2020, per Spotrac.
The expectation is this offseason will reset the market for tight end contracts with Kittle, Philadelphia Eagles star Zach Ertz and free agent Austin Hooper likely to receive lucrative new deals.
Per Over the Cap, among current tight end deals, Travis Kelce of the Kansas City Chiefs currently has the largest total value at $46.8 million. Trey Burton of the Chicago Bears has the most total guaranteed money ($22 million).
San Francisco had a breakout year in 2019 with a 13-3 record and an appearance in Super Bowl LIV. Kittle is arguably the team's best all-around player because of his receiving and blocking skills.
A fifth-round draft pick by the 49ers in 2017, Kittle has far outplayed his first contract. He has recorded more than 1,000 receiving yards in each of the past two seasons, including a tight-end record 1,377 yards in 2018.