The Sun says the Welsh club are pondering a sale before the domestic transfer window shuts this week.
But Foxes boss Brendan Rodgers would prefer to swoop in January or next summer.
Rodgers has just captured young Frenchman Wesley Fofana from Saint Etienne and wants to bed him in before signing another central defender.
But Rodon would like to play in the Premier League as soon as possible.
Tottenham have bid £7million plus extras for the 22-year-old but will have to increase that dramatically as Swansea are looking for around £20m.