Brooklyn Nets owner Mikhail Prokhorov, while focused on selling a minority stake in the franchise, has warmed recently to the possibility of offering a controlling slice of the team, sources close to the situation said.

The change of heart comes after the initial reaction to the minority stake sale was weak — and with interest in the Houston Rockets sale heating up, one source said.

The Nets believe some of the suitors who look at the Rockets will also take an interest in them, sources said.

“As word gets out about the new Nets process, some of the Rockets interest may spill over,” a source said.

One source of investment cash, from wealthy Chinese investors, is of particular interest to both the Rockets and the Nets.

The Rockets, thanks to the eight-year career of center Yao Ming, one of the more popular athletes in China, are the most popular NBA team in that country.

The Nets popularity in China is fast-growing — owing to their point guard Jeremy Lin, sources said.

“A lot of Chinese money will look directly at Houston,” a sports industry source not directly involved in the Nets or Rockets sales said.

Prokhorov has been unsuccessfully trying to find a buyer for 49 percent of the Nets for nearly a year.

In recent days, Prokhorov got approval from the NBA Finance Committee to split the corporate ownership of the Nets and Barclays Center. That will make it easier to sell the team — as this season the Nets for the first time since moving to Brooklyn in 2012 may turn a profit.

Barclays Center, deep in debt, is not assured of a profitable year, a source said.

Meanwhile, the Rockets announced last week they were for sale. They are seeking $2 billion, sources said.

Prokhorov has been aiming for a similar valuation.

Having a Nets controlling stake on the market would not help the Rockets realize their best price.

Mike Zavodsky, the Nets Executive VP of Global Partnerships, is in China this week with 20 meetings lined up.

“Our brand in China is growing, in merchandise sales and commercially,” Brett Yormark, CEO of the Nets and Barclays Center parent company, told The Post.

The Nets financial turnaround has been dramatic since three years ago when the team lost about $150 million.

The improved financial conditions comes largely from an increase in its new 10-year media deal with the Yankees Entertainment and Sports Network (YES) that, starting this season, pays the team $50 million — about double the prior amount — and from reducing payroll, sources said.

“They don’t have those albatrosses around their necks of high-paid contracts for non-performing players,’’ said capital markets expert Marc Ganis. “[Being profitable] would be a big deal. That’d be turning a corner.”

The picture is less bright at Barclays.

Standard & Poor’s on June 22 said the arena’s finances had declined relative to its expectations — largely due to a $6 million loss from guaranteeing money to the NHL’s New York Islanders and some reductions in premium suites and sponsorship revenue.

A Prokhorov spokesperson declined comment.