Argyle face a petition from HM Revenue & Customs and have until December 8 to clear their debts.
The club's bank account has been frozen and both its playing and office staff have not received their salary pay for November.
Synan, who became a director at Home Park in July 2009 and owns a 38% share in the club alongside Japanese businessman Yasuaki Kagami, told BBC Devon: "I'm personally not worried and, at this point in time, we see no reason as to why we can't work our way out of this problem.
"I'll be here in Plymouth as long as it takes to get this issue sorted out. Mr Kagami and I are 100% committed to working together with the board to put together a long-term plan."
Synan also confirmed that former Leeds and Cardiff chairman Peter Ridsdale was helping Plymouth work towards a solution, adding: "He [Peter Ridsdale] is involved in the negotiations, helping us and adding advice."
Source: PA
Source: PA