"It's a decision which I welcome," Khan said at a press conference in Karachi.
"It will help boxers and if I am permitted as per rules and from my promoter then I would love to compete for Pakistan. I will be very happy if I can compete in the Olympics. I want to serve Pakistan."
Khan's father, Shah, hails from a village close to the capital Islamabad but migrated to Britain, where Amir was born in 1986.
Pakistan Boxing Federation secretary Iqbal Hussain said he was thrilled at the prospect of Khan representing the country.
"I have to check the rules whether Amir can compete or not but it would be a huge boost for us if it happens because he is our hero," he said.
Khan's younger brother, Haroon, was blocked from representing Pakistan at the 2012 London Olympics as he had represented Great Britain at junior level.