The Championship outfit are still seeking a permanent manager after Felix Magath was dismissed last month following the club's dismal start to the season.
Under Symons, Fulham have enjoyed a mini-revival and have won their last three matches in all competitions, including the comprehensive victory over Dougie Freedman's men.
It was announced earlier this week that Fulham owner Shahid Khan had named a five-man panel consisting of former players Danny Murphy and Brian McBride, academy boss Huw Jennings, ex-Sunderland striker Niall Quinn and season-ticket holder David Daly to help select a new manager.
Fulham fans showed their support for Symons by chanting his name in the Bolton win and the former Wales international reaffirmed his hope of being offered the role.
"That performance and result certainly won't do me any harm," Symons told reporters.
"When I took over I tried to galvanise the club and get everyone pulling together, and to start winning games, and on both counts it's going pretty well so far.
"It's a great feeling hearing the fans sing my name. I've had stadiums booing me before, when I played, so it's nice to have one cheering me now."
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