Speculations were that Stead wants Kane Williamson to be removed as New Zealand captain.
Speculations were that Stead wants a leadership change in the Kiwi set-up, backing Tom Latham to take over instead. However, talking to stuff.co.nz, Stead said there are no plans for any such move happening.
"Kane and I have a really strong relationship, and we spoke about it. There was no basis in truth and the disappointing part is it's coming from somewhere and someone, but it's not Kane and it's not I," he said.
"I really enjoy working with Kane. The discussions we have are robust and always directed at what's best for the team, which is something I know we are truly aligned on. It's like any business, you always have positive conflict and if there wasn't, then I'd be worried."
Williamson, whose captaincy had come under scanner following the 3-0 Test series defeat in Australia last winter, reiterated there was no truth in the outside talk and he has always had honest feedback from Stead regarding all things.
"Gary and I have a very good relationship, and we're always honest with each other and keen to challenge each other," Williamson said.
"Ultimately we both share the vision of where we want the team to go and that's a really positive one. How we get there is a constant discussion like in any organisation with leadership. It's a positive thing, and we're happy to have those honest discussions," he added.
Stead, meanwhile, is currently hoping for a contract extension as coach from New Zealand Cricket (NZC). The 48-year-old, whose current term expires in October, took over in August 2018. His so far successful stint, includes the 2019 World Cup campaign where Black Caps came one good moment short of winning the trophy and nine wins in 16 Tests.
"Talks have been pretty positive and, if New Zealand Cricket and the players feel as though I can keep contributing then I'd be interested in continuing on," he concluded.
(Inputs from Cricbuzz)