The 34-year-old, who tested positive for steroids in 2013, pulled out of the US Push Championships, a key part of qualifying for the team.
"It was decided that it was in Gay's best interest to focus on learning and to watch," said a Team USA spokesman.
Gay's Olympic team-mate Ryan Bailey won his category to close on a team spot.
Bailey was part of the United States 4x100m relay team that were stripped of their Olympic silver medal from London 2012 because of Gay's positive test.
Bailey, 27, said in August he was "not over" the quartet's disqualification and admitted there is "still some tension" between him and Gay.
Bailey also won August's preliminary Push Championships on dry land in Lake Placid, New York, but Wednesday's event was his first attempt on ice.
He said: "It's a lot faster on ice. It wasn't too much different at the start, but once it hit the crest and started going downhill the sled picks up speed really fast. I tried to think to myself, 'Run faster, run faster.'
"I knew it would be tough, but after the first few pushes I thought, 'alright, I might have a good shot'. To actually win the first year, it's a pretty good feeling."
Gay, who has competed at the last three Olympics, is the joint second fastest 100m sprinter in history.
Only three-time Olympic champion and world record holder Usain Bolt has run quicker than Gay's 9.69 seconds - a time matched by Bolt's fellow Jamaican Yohan Blake.
At the Rio Games Gay was part of the US team that finished third in the 4x100m relay, only to be disqualified for an illegal baton exchange. Bailey failed to qualify for the team.
Legendary 400m hurdler Edwin Moses and Lauryn Williams, the first American woman to win a medal at both the summer and winter Games, have also tried to move into bobsleigh after an athletics career.
Former world 100m champion and convicted doper Tyson Gay has ended his attempt to join the United States bobsleigh team for the 2016-17 season.