The report claims that the Swans have identified the Argentine striker as a potential replacement for Andre Ayew and Bafetimbi Gomis and are set to launch a bid in the region of £10 million.
Ulloa joined the Foxes in the summer of 2014 from Brighton and Hove Albion, yet during his two years at the East Midlands club he has spent the majority of the time on the periphery of the first XI.
Leicester have been busy this summer as they prepare for a Champions League campaign, and one of their main additions has been the signing of forward Ahmed Musa from CSKA Moscow.
With Jamie Vardy, Riyad Mahrez and Shinji Okazaki also on the books, Ulloa will find playing time restricted further this coming season which has prompted questions over his future.
Swansea lacked a suitable target man last season as they failed to replace Wilfried Bony appropriately and Ulloa, 29, has the ideal attributes to make a positive impact at the Liberty Stadium.
The Swans will be hoping to build on their good run of form towards the end of last season and challenge for a top 10 spot in the Premier League in Francesco Guidolin’s first full campaign in charge this term.