The the £15m Spanish striker has yet to make his debut for the club because of a thigh injury and manager Francesco Guidolin says the 23-year-old is still getting up to speed.
"Borja has to go slow for two, three days," Italian Guidolin said.
"He's not injured, but he has to go slow.
Guidolin added: "I hope to have him available for the bench for Sunday, but I'm not sure at the moment."
The Swans boss also suggested 22-year-old defender Alfie Mawson is close to making his first-team bow after joining from Barnsley.
"He is a young player, but I like him and I think he is almost ready to play in the Premier League," said Guidolin.
"I think he will be a good surprise for our fans, for our club."
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Swansea City record signing Borja Baston is unlikely to be ready to start against Chelsea in the Premier League on Sunday.