London’s suggestive skyline already boasts a Gherkin, a Walkie Talkie and a Cheesegrater. Soon they may be joined by the Golf Ball. According to plans seen by the Guardian, a giant glass sphere taller than St Paul’s Cathedral could be built next to the Olympic park in east London.

The design for the concert venue was commissioned by the Madison Square Garden Company, which also owns the New York Knicks basketball team. MSG’s executive chairman, James Dolan, was recently accused in a US court filing of knowing about Harvey Weinstein’s alleged predatory sexual conduct. Dolan is also a financial supporter of Donald Trump.

Early designs circulating for the orb suggest the venue could accommodate up to 20,000 people. Such a size would allow it to rival the O2 arena in the former Millennium Dome in Greenwich, which is operated by another US entertainment company, AEG.

According to sources, MSG has commissioned Populous, the architects behind the nearby London Stadium, Wembley and the planned Bristol arena, as well as stadiums across north America.

One design visualisation shows that the lower half of the orb would be fitted with tiered seating, while the upper half would form a spectacular vaulted roof. A tripod of pylons would elevate the illuminated sphere above the ground, allowing visitors to use pedestrian concourses beneath the venue.

One source said the building could reach 130 metres (427ft) – comparable in height to the arch of Wembley stadium and 20m taller than St Paul’s.

The designs have yet to be submitted for consent to the London Legacy Development Corporation, the planning authority for the Olympic park area. But they appear to be in tune with the LLDC’s policy that the carpark site should be used for “large-scale town centre use with supporting elements”.

However, property industry sources said the site could accommodate up to 1,400 new homes, and campaigners are expected to oppose the plan because of a shortage of affordable housing in the area. The London borough of Newham, where the orb would be built, has 25,079 households on its housing waiting list.

Neither MSG nor Populous would confirm or deny their involvement in the proposal, although blueprints seen by the Guardian bear the MSG logo. A spokeswoman for MSG in New York said: “We do not comment on rumour or speculation.” A spokesman for Populous said: “There’s nothing for us to say.”

A previous proposal to build a “snow dome” ski centre on the site, backed by the former London mayor Boris Johnson, was scrapped in 2016.

It remains unclear when the orb designs were drawn up or how likely they are to be advanced. The owner of the site is currently registered as Westfield, which operates the shopping centre directly to the west of the proposed venue. Westfield said it was “not able to comment”.

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If it goes ahead, the venue would be MSG’s first outside the US. The company also operates Radio City Music Hall in New York and the Forum in Inglewood, California, as well as Madison Square Garden in Manhattan, which has hosted Elvis Presley, John Lennon, Led Zeppelin and Simon and Garfunkel.

MSG’s Dolan was a board member of the Weinstein Company in 2015-16, and in December he was named in a class-action lawsuit filed by six women against the film producer Harvey Weinstein. The suit alleges Dolan “knew of Weinstein’s pattern and practice of predatory sexual conduct toward women from his personal relationship with Weinstein and his position as a director of [the Weinstein Company]”.

A spokeswoman for Dolan has previously said he was “confident that he acted appropriately in all matters relating to his time on the Weinstein board”.

Dolan is a well-known backer of Trump and has donated to a fundraising committee called Trump Victory. He sent Radio City Music Hall’s Rockettes dancing group to perform at the US president’s inauguration.

A spokeswoman for the LLDC said: “We are not in formal pre-planning discussions with any party about this site. Since the termination of the previous publicised plans for a snow dome, we have received no full applications nor held any pre-app discussions.”