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."
Dundee are continuing to work towards moving away from Dens Park to a new stadium in the city, manager director John Nelms has revealed.