The first Cafe Football opened in London in 2013, followed by a second near Old Trafford in 2015.
The two sportsmen and Peter Lim, owner of Spain's Valencia football club and Singapore-based property developer Rowsley Ltd, are looking at opening the first Cafe Football outlet in Asia in 2017, the spokesperson said.
Neville told Bloomberg News the outlet will be in Singapore.
"We've had fantastic reviews in Manchester, and we are looking for a U.K., Europe and Asian expansion over the next 12 to 18 months to add multiple properties," he said.
Neville told Singapore's Straits Times that the trio would also look at expanding Hotel Football across Asia.
"We have an aggressive roll-out plan for Hotel Football, looking to over 5,000 new rooms over the next five to 10 years. We already have discussions in India, China, Thailand, and Malaysia, as well as other parts of the UK," he said.
Rowsley announced in September that the company will open its third Cafe Football at the National Football Museum in Manchester later this year.
The first Cafe Football opened in London in 2013, followed by a second near Manchester United's home ground Old Trafford in 2015.
In July, Neville and Giggs unveiled plans for a multimillion-pound development in Manchester city centre, including a 200-bed hotel, two skyscrapers and a synagogue.
Neville, a former England full-back, said the project would create 1,300 jobs and regenerate a historic part of the northwestern English city.
Welsh football legend Giggs recently left his assistant manager's role at Manchester United following the arrival of former Chelsea boss Jose Mourinho.