Artistic director Jacky Hardacre says a further meeting will be held later this week with culture secretary Fiona Hyslop following an initial round of discussions with officials.
The company announced last week that it would wind up in the summer after having long-term funding plans rejected by national arts quango Creative Scotland.
The news sparked an outcry from leading actors and an intervention from First Minister Nicola Sturgeon, who told MSPs “all options” would be explored to try to keep the company running.
Ms Hardacre said: “We had a constructive meeting with representatives of the Scottish Government today and discussions are continuing.
“We look forward to meeting with the cabinet secretary, Fiona Hyslop, later in the week.”
A spokesman for the government added: “Officials had a constructive meeting with the Scottish Youth Theatre to discuss their financial position.
“Later this week, culture secretary Fiona Hyslop will also meet with the theatre to continue these discussions.
“We are exploring all available options to keep the theatre running, including a continuing dialogue between SYT and Creative Scotland about any alternative funding streams which might be open to them.”
The government and private sector firm Clyde Blowers have provided direct funding for SYT over the last three years following the rejection of a previous funding bid by Creative Scotland.
Its chief executive, Janet Archer, insists SYT - which costs around Â£600,000 to run - can still apply for “project funding” over the next three years.
But Ms Hardacre has suggested that may not be enough to keep the company sustainable.
Creative Scotland said SYT had lost out in a “competitive process” for regular funding with other youth arts organisations across Scotland.
Speaking before the meeting with the government, she said: “We do understand what the assessment (from Creative Scotland) on our application for regular funding came out with.
At the end of the day, we need to move on from it and have got to save our organisation.
“We’ve got to focus on what we have to do in the very short term to give us long-term sustainability.
“Project is part of a jigsaw of options, but Creative Scotland’s own guidance says that it should not be used for the running costs of organisations.
“It’s shorter-term funding. We need something that’s going to help us maintain our staff and run our building.”