According to Michael Scotto of HoopsHype, the Los Angeles Lakers have indeed discussed the possibility with the Utah Jazz, even looping in the New York Knicks as a third team considering their interest in star guard Donovan Mitchell:
As noted on the latest HoopsHype podcast, the prevailing thought around the league is any three-team trade involving Russell Westbrook would need to include the 2027 and 2029 first-round picks from the Lakers with as few protections as possible.
The Lakers had conversations about joining the Jazz and Knicks a few weeks ago in a potential three-team trade, league sources told HoopsHype.
The proposed three-team trade scenario included Westbrook going to Utah and getting bought out. Utah would send Donovan Mitchell to the Knicks, a combination of two players, including Patrick Beverley and Jordan Clarkson, Bojan Bogdanovic or Malik Beasley to the Lakers, and the Jazz would receive significant draft pick compensation from the Knicks and Lakers. The Knicks also would’ve had to part with veteran salary filler(s), such as Derrick Rose to help make the salaries work.