Symons was appointed Fulham boss on a permanent basis 12 months ago after impressing as caretaker following Felix Magath's sacking.
The Cottagers currently sit in mid-table after narrowly avoiding relegation last term, but the club's hierarchy are seemingly far from convinced that Symons can inspire them to promotion.
Fulham have one of the biggest budgets in the Championship and to sustain that they need to bounce back to the Premier League as soon as possible, after missing out last season despite being one of the favourites for promotion.
Now Fulham are understood to be casting their eye over potential replacements, and HITC Sport understand that Hull City boss Steve Bruce is once again at the top of their list.
Bruce has already been targeted by the club in the past and they could return to the KC Stadium chief and offer him the chance to take charge at Craven Cottage.
Bruce is not on great terms with his own bosses at Hull and that could mean a chance is now there for Fulham to make their move.
In what could be his final game in charge, Symons takes his side to Middlesbrough on Saturday.