Spurs deal-maker Fabio Paratici is in Italy for meetings with a number of clubs as he looks to trim the Tottenham squad and he has good relations with Sampdoria.
Winger Gil, who spent the second half of last season on loan in Spain at Valencia, is expected to again be shipped out again, with Sampdoria showing interest in taking the player to Serie A.
However, Sampdoria will use a meeting to discuss Gil to also bring up defender Rodon, according to Italian daily Il Secolo XIX.
Sampdoria are keen to reinforce their defensive options and are aware that Rodon is surplus to requirements in north London.
Tottenham are claimed to have offered him in a deal to Roma for Nicolo Zaniolo, but the Giallorossi rejected the proposal.
Rodon could yet end up in Italy though, with Sampdoria interested in signing him.
The Wales international could be attracted to the move as he looks to play regular football with the World Cup in Qatar now firmly on the horizon.
