The Swans are keen to add a striker to their ranks in the January transfer window.
The Swans are keen to add a striker to their squad in the January transfer window having struggled in that department this season.
They have managed just 22 goals in 23 league games so far this season, the joint second worst record in the division.
Andre Ayew is currently their top goalscorer with eight goals to his name, with first choice striker Bafetimbi Gomis only having managed five so far.
That has led them to seek out reinforcements in the January transfer window, and Gabbiadini was thought to be chief among their targets.
They had already had two offers in the region of £15million turned down, and have now decided to not return with an improved bid after seeing Wolfsburg’s offer of £19million also refused, reports the Mirror.
New manager Francesco Guidolin is now likely to turn his attention elsewhere, add one option could be Crystal Palace striker Dwight Gayle.
The forward is free to leave Selhurst Park this month, and the Swans are thought to be leading the race for his services, according to Sky Sports.