Bannatyne Health Club, on Marvels Lane, has submitted a planning application to Lewisham Council to replace its current tennis courts with three competition-standard padel courts.
If approved, these new facilities will have synthetic playing surfaces, strengthened glass surrounds, and floodlighting, with canopies for year-round play.
Padel, a combination of tennis and squash, has over 25 million active players worldwide.
Last year alone, 15,000 new courts were built in Europe.
The sport is expected to become an Olympic discipline by 2032.
Duncan Bannatyne, chairman and chief executive of the Bannatyne Group, said: “We are proud to be investing in our Grove Park health club with three new competition-level padel courts.
“Padel is a sport that delivers great physical benefits while also being fun and inclusive.
“We look forward to giving our members and the wider community the chance to take part in this exciting global sport.”
Famous fans of the sport include Andy Murray, Jamie Vardy, Annabel Croft, David Beckham, and Nicole Scherzinger.
In addition to the planned padel facilities, the club currently offers a gym, swimming pool, spa, and fitness classes.