The Premier League side are close to a deal for the Ecuadorian, according to reports.
The 25-year-old only moved to the Brazilian side in February from Emelec, for whom he scored 61 goals in 105 matches.
And he appears to have taken his form with him, with six goals arriving in as many outings so far.
Swansea added Italian striker Alberto Paloschi to their ranks in January, though the Jacks could make room for Bolanos by offloading Bafetimbi Gomis this summer, after the Mirror reported in December that the Frenchman was keen to leave the Liberty Stadium.
That said, the pair are different players entirely, with Bolanos standing around half a foot shorter than Gomis at 5ft 7.
And the former, who will reportedly cost £6million, can play in a variety of positions, including out wide or as an attacking midfielder.
Bolanos, who plays alongside Swansea winger Jefferson Montero for Ecuador, boasts an impressive international strike rate too, having scored six goals in 12 appearances to date.
It is unclear whether a change of manager could scupper the Welsh side's hopes of landing the player, with the Sun reporting on Tuesday that caretaker boss Francesco Guidolin is set to leave at the end of the campaign.