David Harker said he had addressed speculation that Durham faced administration at a team meeting.
"Hopefully I persuaded them that the rumours were nonsense," he said.
"We are not running out of money. Work is in hand to sort our long-term future and we looking at ways to continue sustaining cricket in the north east."
He added: "We are not facing administration in the near future."
It is no secret that Durham have been facing financial problems over the past year, with several players receiving offers from other counties.
Opening batsman Mark Stoneman recently agreed to join Surrey for 2017, but it is understood Durham had offered him a six-figure contract to stay.
Batsman Scott Borthwick has also been offered a new deal and is considering remaining, while captain Paul Collingwood recently penned a one-year contract extension.
On Wednesday, Durham will announce that one of their senior players is signing a new contract, with the county still in the running for their fourth County Championship title in nine seasons.
According to Harker, this is a clear sign that they are not going out of business.
"You always get rumours stated by some agents with ulterior motives," he added.
Durham's players have been reassured by their chief executive that the county is not going bust and that all contracts will be honoured.