Glory are in danger of picking up their third consecutive wooden spoon after their winless start to the season stretched to four games on Friday night.
The 1-0 defeat to Central Coast in Perth means Glory have just one draw and three losses to show from four rounds.
Coach David Zdrilic was sacked after just two rounds this season and Griffiths has now overseen a 2-0 defeat to Melbourne Victory and a tight 1-0 loss to the Mariners.
Glory haven't scored a goal since their opening round 2-2 draw with Wellington.
Griffiths has promised to implement a far more attractive brand of football at Glory and although the team is yet to score a goal under his watch, they are at least producing chances.
"I would love to continue," Griffiths replied when asked about his ambitions to coach the team full-time.
"We need to continue to move in a positive mindset so then we can break this barrier.
"The last few years has been this like heavy weight. We need to lift that weight.
"I believe after the international weekend we have real quality coming back into the team and that excites me."
Western United coach John Aloisi has already ruled himself out of applying for the Glory coaching role, but Ross Aloisi, Patrick Kisnorbo and Nick Montgomery are other names who have been floated as candidates.
Although Griffiths is yet to taste victory, he's enjoying the head coach role and is adamant he is the man to lead the team into a bright new era.
He wants more time in the role to prove he's the right man.
"I love being in this position, to be honest with you," Griffiths said.
"The players are buying in. I can see that.
"Now, it's just about breaking that dam that's blocking us at the moment, and just let it flow.
"I want to just open up and find that, and if the belief is growing we've just got to make that happen."
The Mariners are also yet to make a decision on their head coach role, with Warren Moon filling in admirably as the interim following the pre-season departure of Mark Jackson.
Central Coast have posted two wins and a draw from four matches under Moon, and the 43-year-old is keen to land the role full-time.
"I think they're aware (I want the job)," Moon said.
"But as with any club when you lose your coach on the eve of the season, think it's important not to make a rushed decision and I fully respect that.
"I'm very relaxed about the whole situation."
Glory will be back in action away to the Jets on November 23 following the international break, while Central Coast take on the Wanderers on November 22.
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