Muhammad secured Britain a -80kg berth for Rio with victory in the World Taekwondo Grand Final on Sunday.
Sansum won a world silver medal in May but lost to Muhammad in October.
"Lutalo has done an exceptional job but Damon has also done an exceptional job in winning the world silver medal," said GB performance director Gary Hall.
"It is a tough decision and it is such a shame that we are not able to select them both. But we are building a programme in Manchester which is designed to make these kinds of decisions possible."
Muhammad did not go to the World Championships because of a knee injury.
"I have had my challenges this year but I have come back to book the spot for GB," said the 24-year-old.
He and Sansum, 28, will find out before June who has been selected.
Muhammad was controversially chosen ahead of then world number one Aaron Cook for London 2012.
His selection was approved by the British Olympic Association after a bitter legal battle and he went on to secure bronze.
Cook, 24, subsequently defected to fight for Moldova and lost out to Muhammad in Sunday's final in Mexico City.
Great Britain Taekwondo selectors know they face a "tough decision" when they choose between Damon Sansum and Lutalo Muhammad for the 2016 Olympics.