The 20-year-old has scored five goals in 10 appearances this season for the Swans in his first campaign in the top flight, following a successful season with Bristol City in the Championship.
Blues boss Antonio Conte is hopeful of improving his squad during the winter window, but will have to do without the England Under-21 international after the club failed to insert an automatic recall clause in the deal that took him to south Wales in July 2017, according to The Evening Standard.
The only terms under which Abraham can return to Chelsea is if he fails to reach a minimum number of appearances during the first half of the campaign. But having reached double figures while scoring twice against Huddersfield Town at the weekend that threshold is close to being eclipsed.
Abraham's absence comes amid mounting evidence that Conte has a lack of trust in Michy Batshuayi, whose only goals this season have come in cup competitions. The Belgian led a blunt Chelsea attack in the 2-1 loss at Crystal Palace at the weekend in place of the injured Alvaro Morata, but failed to make an impression.
Morata is set to return from a hamstring injury, suffered against Manchester City, when the west Londoners welcome Roma in the Champions League. The Spain international has already netted seven times this term since joining from Real Madrid and will make a much-anticipated return to the first team for the Premier League champions.
Having scoring 26 goals in the second tier last term and had an encouraging start to the 2017-18 season, Chelsea have earmarked Abraham as the future leader of their attack and he is expected to be reintegrated into the squad next season.
But having to wait another six months to use Abraham will force Conte into the transfer market in January in an effort to enhance his attack. Fernando Llorente turned down a move to Chelsea in the summer in favour of joining Tottenham Hotspur on deadline day in the summer, meaning the Italian is keen on making a fresh attacking addition.