Abraham, who is at the Liberty Stadium on a season-long loan from Chelsea, suffered a back injury in Saturday's 2-0 loss at Burnley, leaving the field on a stretcher after attempting to play through obvious pain.
The 20-year-old is Swansea's top goalscorer with four Premier League strikes this season — although he has not scored since October 14 — and Clement believes Abraham will be available for a crunch clash against the Cherries as he does not appear to have sustained any damage to his back.
"Tammy didn't train today [Tuesday] but we are expecting him to rejoin training this week," Clement said of the new England international.
"His back went into spasm at Burnley, but I don't think there is an injury there.
"He is a bit stiff at the moment, but we think he will be okay for Bournemouth."
Swansea sit 19th in the Premier League, having lost seven of their last eight games in all competitions.