Tiffany is drawing up a radical plan to move out of its famous Fifth Avenue flagship while it undergoes a massive renovation. The solution: It will set up shop next door in the meantime.

Sometime next year, the swanky jeweler plans to conveniently move its flagship operation just around the corner to 6 E. 57th St., a 36,000-square-foot space recently vacated by a big Nike store, sources told The Post.

Details around the scope and timing of the plans are still being nailed down. But some insiders estimate the renovation project could take years and cost millions of dollars.

In 2001, luxe-goods purveyor Tiffany began a renovation of the 124,000-square-foot Art Deco store that lasted three years, with Yabu Pushelberg collaborating with the store’s in-house designers.

In May, the company said earnings surged more than 50 percent as sales rose 15 percent. Executives signaled higher investment spending in technology, marketing communications, visual merchandising, digital and store presentations.

At that time, CEO Alessandro Bogliolo said Tiffany would be renewing its product offerings and enhancing in-store presentation as well as “delivering an exciting omni-channel customer experience.”

The space at 6 E. 57th St. is attached to the side of Trump Tower and owned by the Trump Organization, which has approved the deal. Tiffany, however, won’t be leasing directly from the Trumps but rather from SL Green Realty Corp. and Jeff Sutton, the owners of Nike’s newly opened flagship at 650 Fifth Ave., who had agreed to take over its long-term, low-rent lease. During its own prolonged space search, Nike had renewed one of its five-year options that runs through May 31, 2022. Documents show it has two, five-year options remaining in the future, which SL Green may or may not renew.

Andrew Goldberg and Annette Healey of CBRE represented Tiffany in this transaction, with SL Green handling negotiations in-house.

The jewelry retailer opened its doors in 1940 at the granite building designed by Cross & Cross. It was the first structure to include central air-conditioning. Its 8,400-square-foot main floor with 24-foot- high ceilings was designed as a column-free ballroom via three, 106-ton trusses placed between the first and mezzanine floors.

The property was purchased as a trophy by the Japanese company Daiichi Real Estate in 1984 for $14.5 million, with Tiffany finally purchasing its famous home for $94 million in 1999.

As the Nike space still must be spruced up and rebranded, it is likely the store won’t be moving next door until sometime next year.

While its southern side is connected to Trump Tower, it is flanked on its eastern side by 590 Madison Ave., also known as the IBM Building — for its largest tenant — and its public atrium that also flows into Trump Tower.

The owner of 590 Madison, the State Teachers Retirement System of Ohio, has just hired Douglas Harmon and Adam Spies of Cushman & Wakefield to sell the office building, Bloomberg reported, at a price expected to reach $1.3 billion.

Tiffany formally released the news Tuesday evening.