Dome also said the million-dollar sums bandied around in the media weren't even close to the price tag they placed on Burns.
"We didn't put anything like that kind of money on him."
If Shanghai Shenhua, who signed Australian forward Tim Cahill to a hefty contract this week, decided to meet Wellington's demands for Burns and the Phoenix wanted to make the deal, Wellington would need to release Burns from his contract so Shanghai could sign him. It would be a different transaction to a transfer deal during the designated windows.
The Phoenix would then be limited in who they could sign as a replacement given their window has closed. They could only sign off-contract players, which is generally a shallow talent pool.
Wellington would also be loathe to release Burns without adequate compensation given the 26-year-old has scored 10 goals this summer and has been one of the A-League's best players.
One report from across the Tasman recently suggested that Burns, who is in his first season of a two-year deal, had a clause he could exercise to leave the Phoenix at the end of the season for a small fee.
"It's not quite as simple as that," Dome said. "But we can't comment on individual contracts."
Dome said there were two other Phoenix players who had generated interest from overseas clubs but he didn't mention who they were.
Meanwhile, the Phoenix announced tonight they will play two games against the Fijian national team in the Pacific Island nation in June as part of their pre-season work for the 2015-2016 campaign.
The club will travel there courtesy of a new corporate partnership with Fiji Airways and the Phoenix academy team will also play twice against Fiji's under-23 side during the tour.
Phoenix striker Roy Krishna, Fiji's only fully-professional player, has been in top form during the ongoing A-League season with six goals in 11 games. Phoenix coach Ernie Merrick said Krishna would likely play for Fiji during the trip.
The fourth-placed Phoenix next meet the Western Sydney Wanderers across the Tasman on Sunday.