The proposals include a subterranean gym, pool, sauna and wine store beneath the Grade II listed venue.
The five-star hotel, which opened in the 1800's, is also planning to build two new rooftop levels with 40 extra bedrooms.
Claridge's owner Maybourne Hotel Group said in the design statement that while the hotel was ‘world class’ its current fitness facilities were ‘minimal’ and often ‘disappointing to many international customers’.
It added that the extension was necessary as the hotel’s 197 rooms were normally full and it often had to turn down visitors.
“To maintain the hotel’s high profile…Claridge's needs to focus on its immediate requirements and look ahead to the next 50 years,” said Maybourne.
The plans are subject to approval by Westminster City Council, but it is understood that the hotel will remain open if the construction is approved.
Claridge's said in a statement: “Claridge’s is excited about our future development plans to put in to place state of the art, sustainable technology and systems which will further enhance services for our guests, staff and neighbours, taking this iconic Mayfair hotel’s vision into the next century.”