Andrew Simpson, known as Bart, was killed when Team Artemis' catamaran capsized in San Francisco Bay during training for the competition in May.
There has not been a British victory in the competition's 162-year history but now Sir Ben is to hold talks within "a matter of weeks" over the possibility.
Keith Simpson said: "He (Andrew) would have loved to have been involved in an America's Cup British challenge.
"I think it's what he would have always have wanted and yes, I think it would be great for the British challenge and I think they've got the right people involved if they can get together and get the money to do it."
It has been suggested that any prospective British boat in the competition could be named 'Bart' - Andrew Simpson's nickname after the cartoon character.
Keith Simpson said: "That would be great. I would be very proud."
Strategist Ainslie, whose team recovered from 8-1 down to beat Team New Zealand 9-8, dedicated Oracle Team USA's extraordinary win to Simpson.
Quoted by the Daily Mail, Ainslie said: "I looked up to the stars after it all settled down at the end and thought of Bart. In some ways this was for him. He loved sailing and he loved the America's Cup. He would have been so excited about this series."
Mr Simpson told ITV News the touching tribute made him feel "proud because he is a brilliant sailor and the fact that he can spend time devoting it to Andrew is great".