Parker and his Craven Cottage side were relegated from the Premier League into the Championship this past season.
According to talkSPORT, Parker may have concerns about player recruitment at Fulham.
He may believe the Bournemouth job represents a better chance for him to get a team back up to the Premier League.
"His opinion isn't sought after as much as he would get somewhere else.
"He found that last season where there were a few issues regarding certain players he wanted.
"If you don't feel like your input is valid, I'd rather go somewhere with a smaller budget."
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