A source has told Sky Sports News that a deal is being considered for the 22-year-old, with a fee between £7m and £18m under discussion.
All the done deals on Deadline Day
The deal does not have to go through on Monday because the domestic window remains open until October 16.
The centre-back has also been drawing interest from West Ham.
Rodon has been at Swansea throughout his professional career, apart from a loan spell at Cheltenham in 2018.
He has already been capped four times by Wales and has been a regular in the Swansea defence this season as they have made an impressive start to the Championship campaign.