The English Premier League side have submitted two separate offers for the 18-year-old forward, who netted over 30 goals for the Easter Road side’s Under-20 team last season, but Cummings is understood to be happy at Hibs.
Cummings, who scored both goals in Hibernian’s 2-0 win over Hamilton in the first leg of the play-off in May, missed his penalty in the shoot-out after Accies had won the second leg 2-0 at Easter Road.
But Hibs have rejected both bids from the Swans, with the second believed to be a six-figure sum.
Swansea have already snapped up Scottish talent in former Hearts midfielder Adam King, and Falkirk duo Stephen Kingsley and Jay Fulton.
Cummings was with Hearts as a boy, but was released by Hibernian’s capital rivals after sustaining a serious injury and undergoing surgery on his cruciate knee ligament.
He joined Hibs in August 2013 after a successful season with Hutchison Vale.