New Swans boss Francesco Guidolin is an admirer of Paloschi and has turned his attention to the forward after being priced out of a move for Napoli's Manolo Gabbiadini.
One man Swansea have managed to bring in is Falkirk midfielder Ryan Blair.
The 19-year-old has signed a three-and-a-half year deal at the Liberty Stadium and will join the club's Under-21 setup.