Each of Radio Taxi's 2,500 drivers stand to make about £5,000 each if they back a deal to change its status to a private company.
It will involve US businessman Brian McBride taking a 26% stake in the business and the remaining shares will be spread between drivers and staff.
The company was established more than 50 years ago by a group of six independent licensed taxi drivers and has the second largest fleet of taxis in London behind ComCab.
The deal will raise more than £10 million to enable it to expand its fleet beyond black cabs into other forms of personal transport such as chauffeur driven cars, couriers and shuttle buses.
Bosses also plan to improve key technology that supports internal billing and management information systems.
The company said it will create an internal market for share trading to prevent the company attracting any outside takeover offers. It will host an emergency general meeting on May 16 and at least 75% of drivers must back the plans for them to succeed.
If they vote for the change, Radio Taxis' 2,500 drivers will each get a windfall worth about £5,000, comprising £1,100 cash plus 1,000 shares.
However, it is reported that some drivers vehemently oppose the scheme, with the Transport and General Workers union launching a 'vote no' campaign.
McBride is head of US-based Yellow Cab Company and will invest £2 million in equity and £1.5 million in loan reserves under the terms of the deal.
He said: 'I have always been particularly impressed with the commitment of the management team, the technology employed by the business and the sheer quality of the drivers.'
If members do approve the move, Dial-a-Cab will be the last remaining mutual taxi company left in London.