Roden, 24, has struggled for game time at Spurs and even more so since the arrival of Antonio Conte.
Albion head coach Graham Potter previously worked with Rodon during their time together in the Championship at Swansea.
The centre back signed for Spurs in October 2020 for £11m - rising to £15m after add-ons - and is contracted with the North London club until June 2025.
Brighton have struggled with injuries of late in defensive areas, with influential skipper Lewis Dunk set to be out until mid February with a knee injury.
Adam Webster has also had his injury issues this season plus last summer the Seagulls lost star man Ben White to Arsenal in a £50m deal.
Brighton could potentially land Rodon for around £10m and Newcastle United and Leeds United are also said to be keen on the former Swansea man.
But Potter insists he is comfortable with his options and said the defensive area will not be a priority this January.
"It's not an area we're looking to strengthen," said Potter. "Because of the players we have, but you never know what the window does, so it's not completely disregarded, but it isn't a priority."
Brighton also have defensive cover available with loan players currently performing in the Championship. With the likes of Matt Clarke at West Brom, Leo Ostigard at Stoke and Jan Paul van Hecke at Blackburn.
"The loans, you've got to look whether it's right for them to be recalled, whether it's possible for them to be recalled," Potter added.
"Sometimes the loan is there until the end of the season, sometimes you've got an option to bring them back in January.
"In that situation I can't see anything changing really."
Brighton have plenty of players out on loan but remain reluctant to use this January window to bring in loans - despite covid uncertainty.
"It's something we'll discuss as a club. As a general rule, it's not something we're overly keen on doing, because obviously that means the guys we have aren't getting game time.
"That isn't best for us, generating future development.
"But you've always got to keep looking, what's the best solution, be open-minded. I don't think we're that shut off to things, but as a general rule I understand why that hasn't been our avenue of strengthening."