The London Eye could close down after being served an eviction notice after a £1m rent demand - an increase of more than 1500%.
The London Eye is one of the capital's top attractions
Its landlords, the South Bank Centre (SBC), said they are not getting enough rent from the land that holds part of the wheel's supporting structure.
If the rent is not paid they say the Eye will have to be removed in a month.
None of the parties wished to comment but said negotiations are taking place in the hope of reaching a settlement.
According to a document seen by Kate Hoey, MP for Vauxhall, SBC sent out the eviction notice after issuing a demand for the increased rent.
She told BBC Five Live: "The South Bank Centre, a public company, are just being very, very greedy.
"A tiny bit of the London Eye, one of the legs sits in the Jubilee Gardens which was given to the SBC for a pound when the Greater London Council broke up.
"I hope the secretary of state, who knows about this now, gets involved because it is true they [SBC] have sent a legal letter saying if the negotiations are not settled by 1 July the Eye will have to be removed.
"I think we all know this won't actually happen but it just seems amazing."
The 450-foot wheel, which is operated by British Airways, is one of London's top tourist attractions.