The 24-year-old is on the radar of many clubs in England and reports down south suggest the Swans are preparing a big-money offer for the former Raith Rovers and Partick Thistle star.
However, Easter Road officials have not had contact from their counterparts in south Wales.
Hibs are keen to keep Nisbet at the club and are in talks over a new contract for the striker. They are also keen to bolster their attacking options, with Christian Doidge and Jamie Murphy on the treatment table.
Nisbet was the subject of a £3 million offer from Birmingham City in the January window which Hibs rejected. The 24-year-old handed in a transfer request at the time but is once again settled in Leith and was included in the Scotland squad for the upcoming World Cup qualifying triple-header.