Rhyl's Belle Vue Stadium hosted matches in this season's Europa League qualifiers
Rhyl FC say "significant external investment" is needed if the club is the survive the financial impact caused by the coronavirus.
The Lilywhites agreed monthly payments for their ground, Belle Vue, back in December to cover operation costs.
But now Cymru North games have been postponed leaving the club without significant income for the near future.
"We simply don't have the financial resources to keep things going," said Rhyl's Chairman Paul Higginson.
"Without clarity on external financial support for sports clubs or support from an investor, the only option may be to unfortunately call time on Rhyl Football Club.
"This is a situation which I'm sure many other clubs are facing.
"However, the nature of the ground ownership for Rhyl FC means that our problems are multiplied."