Off-contract coach Fittler is set to front the NSW Rugby League board on Friday to discuss his preferred staff for next year, after two straight series losses.
But Alexander confirmed on Friday morning he would not continue in the job after working alongside his former Penrith teammate Fittler since assuming the role in 2018.
"I've just decided that that's enough," Alexander said on SEN.
"It's been a massive part of my six years. But it's a big commitment and I've committed elsewhere.
"When everything calmed down after the trip overseas, I just thought about it.
"And when Freddy asked me are you good to go again, it's not a job that you (should) hesitate on.
"Freddy wants to continue and I certainly wish him well."
Alexander said he and Fittler had not discussed who might take on the role next year if Fittler retains his job as NSW coach.
Fittler had presented a review of the Blues' 2-1 State of Origin series loss to the NSWRL board last month and had been asked to come back on Friday with his projected staff for 2024.
Andrew Johns, Danny Buderus and Paul McGregor were among the other staff in camp with Fittler this year.
Ivan Cleary also featured in Fittler's box in a game-day role for Origin III and is an option to take on a similar position next year.
Fittler is unlikely to learn on Friday if he will keep the top job for next year, with the board to then discuss his preferences afterwards.
While Fittler is favoured to be offered a one-year extension that is unlikely to be confirmed until the next board meeting in late October.
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