Six months after assuming the CEO position at Sony, Kazuo Hirai is coming under increasing pressure to turn around the sluggish entertainment and electronics giant.

Shares are down 28 percent since the 30-year Sony veteran took over on April 26, the company’s US headquarter, the Philip Johnson-designed “Chippendale” building in Midtown has been put on the block, and nearly $2 billion in acquisitions have come under attack as not addressing Sony’s main problem — a lack of profits.

More recently, Hirai cut Sony’s profit forecast this year by 27 percent, to $1.7 billion — but Wall Street thinks even that pared-down number is high.

With Hirai unable to find the right solution so far, the whisper among a growing number of analysts and bankers is that Sony will soon be forced to sell its lucrative US entertainment business.

Call it wishful thinking or a keen intuition, but at media lunches in Hollywood and New York — and published reports here and there — the possibility is on the lips of most industry insiders.

“Sony’s market cap is $11.9 billion,” said one analyst who has heard the sale rumors. “The entertainment assets alone are worth in excess of Sony’s market cap, possibly more.”

The company denies Hirai is even thinking of such a sale.

“Sony’s entertainment businesses are not for sale,” Jim Kennedy, a Sony spokesman said. “Period.”

Sony USA, run by Michael Lynton, houses a film studio readying the release of the latest James Bond movie “Skyfall,” as well as a TV production house known for its “Seinfeld” library and its vibrant slate of programs, including ABC’s “Happy Endings.”

Then there’s Sony Music, the No. 2 player in the music business.

Revenue at the entertainment division represents 17 percent of sales.

Despite the denial, rumors about a possible sale are hard to miss.

This week, a story in the Hollywood Reporter said Lynton had been approached by Time Warner boss Jeff Bewkes about a potential position there — the implication being that Sony USA will be sold and Lynton would need a place to land.

Another whisper is that the billionaire owner of Warner Music, Len Blavatnik, has his eye on Sony USA.

Blavatnik, though, has not made any overtures yet, sources said.

There was even the rumor last week, passed on by two sources that a financial book on Sony USA is out. Neither said they saw it and Sony denies its existence.

CBS boss Leslie Moonves told the Wall Street Journal this month he’d be interested in bidding if Sony USA were for sale.

Other media executives are said to have traveled to Japan recently to meet with Sony brass about buying the entertainment business.

What can’t be denied is that Sony needs a quick solution to its financial problems.

Moody’s Investors Service isn’t seeing a rosy future for Sony.

In a note an Oct. 12 note, it downgraded Sony’s long-term senior unsecured bond ratings to Baa2 and moved its outlook to negative.

“Demand for games consoles and compact digital cameras is likely to continue to decline due to the integration of gaming and camera functions into smartphones,” it said.