Graham, 41, is considered a senior coach in waiting and is interested in stepping up to take the reins at an AFL club in future.
But it won't be as Adam Simpson's Eagles successor, after Graham joined Dean Cox, Josh Carr and former Collingwood coach Nathan Buckley in pulling out of the race.
Graham on Sunday revealed he had delivered the news to Eagles chief executive Don Pyke.
"I'm really comfortable in what I'm doing at Fremantle and I'm really enjoying the ride that we're on and the journey we're on," Graham told ABC radio.
"I've been given a good opportunity to develop and progress in my coaching here at Fremantle.
"I spoke to Don Pyke during the week and informed him of my decision.
"It is clear I want to coach one day but I am not in a rush and really enjoying my role at Freo."
Graham played 37 games for West Coast between 2005-2008 and was an assistant coach at the club under Simpson.
He joined Fremantle as an assistant to Justin Longmuir in 2022, taking charge of the Dockers' forward line.
"The club has a great culture and we have a really connected group and it is good to be a part of it," Graham said.
"That was the largest part of it really.
"I get opportunities to develop and I am loving working with our young forward line.
"We've some young and energetic forwards who are growing each week and I am really enjoying that ride."
West Coast caretaker Jarrad Schofield claimed his first win from four games in charge with victory over Gold Coast on Friday night.
Schofield was non-committal when asked whether he would apply for the full-time job but is understood to be keen.
"I said the other day, wins and losses - I don't know if they'll mount up or not in terms of whether I'm endorsed," Schofield said after the Eagles' win over Gold Coast.
"But what I do know is it just solidifies why I coach, why I accepted the opportunity to step up as interim.
"I'm here to try and help the team be better, and hopefully I'm doing that.
"We asked the players to do it for longer than last week and they did that and if they're listening to the message, fantastic."
West Coast 2018 premiership coach Simpson was told last month told his services were no longer required, after winning just 10 of his final 70 games in charge.
Former Eagles forward Ash Hansen, Brett Montgomery, Daniel Giansiracusa, Scott Burns and Andrew McQualter are among the other potential candidates to take over.
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