Gasol professed his love for the Grizz and said, "If they think it is best, I would do anything for this franchise."
The 32-year-old veteran made it clear he isn't seeking a trade, though, saying, "I have a responsibility to this city. I'm not gonna quit, no matter what."
Memphis is 14th in the Western Conference at 8-19, and it is in danger of missing the playoffs for the first time since 2009-10.
Per Spotrac, Gasol is in the midst of a five-year contract that will pay him more than $46 million in total over the next two seasons. A player option kicks in for 2019-20, meaning Gasol could opt for free agency.
The Grizzlies fired head coach David Fizdale in November following a 7-12 start after he spent less than two seasons on the job.
That gave rise to speculation that a rift between Gasol and Fizdale led to the coach's firing, but Gasol said he didn't request the move, according to Ronald Tillery of the Commercial Appeal.
Per Basketball Reference, Gasol is the best player in franchise history with 71.0 win shares, which places him ahead of point guard Mike Conley and his 63.4 win shares.
This season Gasol is averaging 19.0 points, 8.6 rebounds, 4.2 assists and 1.4 blocks per game, and appears well on his way to his fourth career All-Star nod.
The 2012-13 Defensive Player of the Year is the face of the franchise in Memphis, but it hasn't shied away from making some tough decisions recently, including allowing popular players Zach Randolph and Tony Allen to leave via free agency during the offseason.
Trading Gasol would likely bring in some key pieces for a rebuild if the Grizzlies decide to go in that direction.