CUPERTINO — First, its 2015 opening was pushed back a year. Now it appears Apple’s (AAPL) iSpaceship headquarters could come in over budget.

Two billion dollars over budget.

According to a report from Bloomberg Businessweek on Thursday, the architectural creation hailed by Cupertino officials as “unprecedented” and “truly a legacy building” after it was famously announced by then-CEO Steve Jobs in 2011 may ultimately pencil out at $5 billion. Citing unnamed sources, Bloomberg said that compares with an original cost estimate that sources put at $3 billion.

Apple has never publicly shared any budget estimates for the project, and the company would not comment on the report. It’s been clear for years now that Apple would need much more space to accommodate its burgeoning workforce than its current headquarters at One Infinite Loop can handle. And the fact that the land for the new building has mushroomed from the 50-acre property first announced in 2006 to the 175-acre facility Jobs announced in 2011, it’s no surprise that Apple’s construction bills could be higher than first planned.

“I haven’t heard anything from Apple to suggest the costs have gone up dramatically or that they’re planning on scaling back,” said Cupertino Councilman Mark Santoro. “As far as I know, they’re still planning a building similar to what Steve Jobs first announced. He was a visionary and very hard-driving guy. And when someone has to actually implement a spectacular building like that, unlike anything else in the world, it may take more time and money than first thought.”

Neither Apple nor Cupertino officials immediately responded for comment, so it’s hard to say how much truth there is to the Bloomberg report. But while cost overruns are commonplace on outsize projects like this, Jobs’ vision of an extravagantly designed headquarters with dramatic curved-glass walls and exotic wood paneling certainly could now be more politically challenging to pull off, especially if it’s perceived as wasteful or over the top.

“It would take some convincing for me to understand why $5 billion is the right number for a project like this,” Keith Goddard, CEO of Capital Advisors and a big Apple shareholder told Bloomberg. “This is rubbing salt in the wound, to spend at a level that most anyone would say is extravagant, at a time when they’re being so stingy on dividends.”

While Apple products continue to capture the world’s imagination, the company has struggled in the nearly two years since Jobs unveiled drawings of the spaceshiplike design. Back then, Apple shares stood at about $332 and they’d rise steadily to reach a record closing high of $700.10 last September. Since then, the stock price has tumbled, prompting grousing and even legal action by some shareholders who are pushing Apple to share some of its huge pile of cash through fatter dividends.

The Bloomberg report said Apple has delayed the start of construction as it works with its lead architects to cut $1 billion from the budget. Apple may also be competing for subcontractors with other local developments, such as Facebook and Google’s (GOOG) new headquarters and the San Francisco 49ers stadium under construction in Santa Clara.

While the true cost of the project may never be publicly divulged, reports of Apple’s launch delay and cost concerns raise the question: With both Jobs and his ability to pitch his grandiose vision gone, might CEO Tim Cook scale back the plans? Analyst Trip Chowdhry with Global Equities Research says he hopes not.

“Apple has to keep thinking big,” he says. “Silicon Valley is a place where we don’t shy away from taking risks, even if you have to spend more money than you first thought. I’d tell Tim Cook ‘full speed ahead and make the biggest and best headquarters you possibly can.'”

Contact Patrick May at 408-920-5689 or follow him at Twitter.com/patmaymerc.