The former Fulham defender was put in temporary charge of the team on Thursday after Felix Magath was sacked by chairman Shahid Khan following their terrible start to the Championship season.
After seven matches, the side relegated from the Premier League last season are rooted to the foot of the table with just one point and a minus 12 goal difference.
Symons will take charge of their clash with Blackburn Rovers at Craven Cottage on Saturday and believes he is ready to succeed Magath in the long term.
"I've done caretaker roles a few times, and other jobs at football clubs, and it [being a permanent manager] is certainly something I feel I'm ready to do now," the 43-year-old said on Friday.
"It's been a difficult time for the football club, there's no getting away from that, you can't escape one point out of 21.
"Everybody craves stability at Fulham and I aim to give that.
"I want to play a settled side as much as possible but the games comes thick and fast so you will need to use a squad, but I certainly think certain areas need to be settled for sure."
Symons has stepped up from his manager role with Fulham's under-21 side to look after the first team and reportedly faces competition from the likes of Tim Sherwood and Neil Lennon for the full-time role.