Smith has named Cameron Norrie, Dan Evans, Andy Murray and Neal Skupski for the group clashes against Australia, France and Switzerland, as Britain bid to reach the finals.
But the efforts in New York of Draper, who is into the fourth round of a slam for the first time, may mean Smith adds the 21-year-old to his squad.
“We’ve got four, we might take a fifth,” said Smith, who was keen to watch Draper and also judge Andy Murray’s fitness after his abdominal injury leading into the US Open.
Murray lost in the second round at Flushing Meadows last week but seemed fully fit.
While the former World No1 suggested he might not merit a place in the side due the way he played in losing in straight sets against Grigor Dimitrov, Smith is likely to keep him.
“The four won’t change in terms of who’s named unless something happens here,” Smith said. “It’s a question of do we add to it or not?”
Evans said he had messaged Murray to tell him he was needed in the team, but whatever Smith decides he will also have a hard choice in terms of who plays singles.
Manchester is hosting Davis Cup tennis for the first time since 1994. Smith said he expects record crowds and a great atmosphere.
“We’re desperate to qualify this time,” he said. “It was hard last time, that wasn’t a great feeling, so we want to make sure we get to the knockout stage this time round.”