The Dark Blues announced last year that they plan to leave Dens Park and build another stadium and training facility at a site near Camperdown Park.
Managing Director Nelms is confident of progress which would see Dundee in their new home within two years.
Speaking to The Courier he said: “We are in negotiations on a couple of different levels that are very important to the whole process. Once we get past those two or three milestones, then we will be off and running.
“We are getting ready to appoint a development partner and we are working on how we are going to enter and exit the site.”
Nelms was effusive in his praise for Transport Scotland and the council, who have been “good to work with” and “supportive” of the process.
Nelms continued: “Ideally, we would like to be in the stadium by the 2020 season. Now whether that is the beginning of the 2020 season or the middle I am not really that bothered.
“I just want it up and running in the right manner and I don’t want to rush it. This is something we need to get right first time so when we go in everybody is excited.”
Nelms is also keen to have what he called “a few dry runs” by staging concerts or other events at the new Dundee stadium before the football season starts - “just to make sure everything is spot on.”
Dens Park ‘like Forth Bridge’
The American also revealed that since he arrived at the club, there had been huge work undertaken in terms of rewiring and replumbing, adding that it costs in excess of £300,000 each year just to keep Dens ticking over.
“That’s not enhancing it in any way for fans coming through, that’s just to keep it standing,” Nelms added.
“We have added things for safety but it is almost like the Forth Bridge – you start [painting] at one end and by the time you get to the other end you need to start over again.
Dundee have a lease agreed with former Dundee United director John Bennett, and have a deal to rent Dens until 2036. But Nelms doesn’t foresee any problems when the time comes for the Dark Blues to up sticks.
“For a long time, John and I have had an understanding of what has to be done with Dens at the time,” Nelms explained. “John has allowed Dundee to be here [during administration] and working through that.
“He has been very good to the football club.”
Meanwhile, the Dark Blues could be playing their football at the Kilmac Stadium at Dens next season, with the club understood to be exploring different avenues for raising income.
Kilmac, a local civil engineering firm, was the club’s shirt sponsor between 2010 and 2013, and again for the 2015/16 season.