John Nelms said on the club's website that a land use application will soon be submitted with the local council for land in Camperdown Park.
He and fellow American owner Tim Keyes recently bought 29 acres of land there, near the city's Ice Arena.
Nelms spoke after the club revealed an operating loss of £530,000 to 31 May.
"They are not great, but they're nothing to worry about," Nelms said of the club's annual accounts, which showed that turnover had remained at about £4m.
"Football Partners Scotland, the major shareholder, funds any losses. We said we would do that from the get go."
Nelms explained that missing out on a top-six finish in the Scottish Premiership - Dundee finished eighth - resulted in £200,000 less income than had been budgeted for.
Club wages also increased by £175,000, partly down to the first pay rises to administration and support staff "for a number of years".
Nelms pointed out that the maintenance bill for Dens Park had risen £50,000 on the previous year and an additional £500,000 would be required in the 2017 accounts because of rent increases.
Dundee's stadium is less than 400 yards away in the same street as city rivals Dundee United's Tannadice Park.
"The biggest issue we have is the stadium itself," added Nelms.
"We've put over £200,000 into the ground and that's not enhancing the ground - that's just keeping it going.
"We assume that those issues are going to get worse and worse as time goes on.
"We are trying to put on a 21st century entertainment product in a 19th century building and it's not new news that Tim and I have bought 29 acres near the ice rink in Camperdown Park.
"And we will be putting in a land use application shortly that we hope really enhances Dundee Football Club."

GKN Aerospace in Yeovil, Somerset, which makes airframes for Royal Navy helicopters, said the potential loss of the contact puts 230 jobs at risk.
Leonardo, which assembles the Wildcat helicopter in the town, has told GKN it plans to take production in-house.
The firm said the current arrangement was "no longer sustainable".
The union Unite said it was a "massive blow".
GKN has begun formal consultations with the unions regarding potential job losses in Yeovil.
The firm said in a statement that the move by Leonardo "puts at risk the long term viability of our Yeovil site".
GKN added: "Having completed a thorough assessment of the business, we have regrettably concluded that GKN Yeovil, as it stands today, is no longer a sustainable business and will have to be significantly downsized or fully closed.
"We will now enter a period of consultation with nominated employee representatives."
Andy Soughton of the Unite union said talk of a potential site closure was a "bit of a shock".
"We've had quite a few redundancies over the years, and work has dropped off a little bit," he said.
"So I think people were expecting something to happen. But not a closure."
More than 250 jobs were lost at GKN's car manufacturing branch in Telford in Shropshire in August.

Hythe Ferry runs between Hythe and Southampton, serviced by a train which runs along a 640m (2,000ft) pier.
The presenter lent his support to a community group's aim to take over the management of the pier and train.
Its current operator said numbers using the ferry had been falling.
Earlier this year, Hythe Ferry Ltd warned staff about possible redundancies, having suffered a "year-on-year decline" in passenger numbers and faced with higher operating costs.
More than 9,000 people have signed a petition calling for the service to be saved.
Peter King, of the Hythe Hythe Pier Train and Ferry Action Group, said members wanted to create a "viable modern ferry" by a charitable trust taking over the management of the Victorian pier and "relieving" the ferry operators of the costs of maintaining it.
He said a redevelopment project could cost £2-3m but a trust would be able to access other sources of finance, including lottery grants.
Mr Snow said: "This train is the oldest running pier train anywhere in the world, so I'm campaigning to keep it open. We need to do everything we can to keep this extraordinary piece of our past running."
Dundee are continuing to work towards moving away from Dens Park to a new stadium in the city, manager director John Nelms has revealed.
[NEXT_CONCEPT]
Hundreds of aerospace jobs could be lost if a factory is forced to "significantly downsize" or close, it has been claimed.
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A Hampshire pier and ferry service facing an uncertain future is a "national treasure" which should be saved, television historian Dan Snow has said.