City are four points above the Premier League relegation zone and they want to sign a striker in January.
Paloschi, 26, has scored eight goals in 21 league games for Chievo this season.
Starting his career at AC Milan, the Italian also played for Parma and Genoa. He joined Chievo in 2011 and has scored 42 goals in 144 Serie A appearances.
Paloschi has represented Italy at Under-21 level, scoring in their 2-1 defeat to Wales at Swansea's Liberty Stadium in 2009.
He lined up alongside the likes of Milan and former Liverpool forward Mario Balotelli in a game won by Aaron Ramsey's spectacular strike.
Paloschi could now be about to link up with compatriot Francesco Guidolin, who was appointed Swansea's head coach earlier this month.
Former Udinese manager Guidolin guided the Swans to a 2-1 win at Everton in his first game in charge, the Welsh club securing back-to-back victories for the first time this season having previously beaten Watford.
Despite the encouraging start to Guidolin's reign, Swansea are still 15th in the Premier League table, with only bottom side Aston Villa scoring fewer goals so far in this campaign.
Swansea City are in talks with Chievo about signing striker Alberto Paloschi for a fee of around £8m.