Greg Wyshynski of ESPN.com passed along comments from Melnyk, who said the market in Canada's capital must "prove itself" to ensure the team's future.
"If it becomes a disaster, yes," he said. "If you start not seeing crowds showing up, yes. But for now, we are on the cusp of doing OK. It's a direct relationship, make no mistake about it, between revenue and how much you spend on players.
"We are one of the biggest spenders in this league. We spend $68 million a year. Everyone says, 'You are cheap.' Are you kidding me? Even at $68 million, that's way too much over a revenue base that we have."
Melnyk purchased the Senators and the Corel Centre, the club's home arena that's now known as the Canadian Tire Centre, for a reported $125 million to $130 million in 2003.
Forbes valued the organization at $420 million in November, with $135 million in revenue and $10 million in operating income.
The Sens rank 22nd in the league in average attendance in 2017-18 at 16,448 fans per game, representing 81.3 percent capacity, per ESPN.com.
Wyshynski noted Melnyk, who's seeking money to either renovate the Canadian Tire Centre or to build a new arena, said he would consider relocation before a sale.
"Imagine if you own a McDonald's franchise, but you can move it," he said. "But why would you sell it? It's something that's very difficult to buy. We're doing OK here. We're not doing great, but we're doing OK."
The comments come with Seattle among the cities interested in an NHL team, with a $600 million renovation planned for the city's KeyArena.