Spurs have been holding talks with Swansea in a bid to reach an agreement for the defender, but the two clubs have different valuations of the player.
The gap has been closed to just £5m, but there is no agreement in place yet and the clock is ticking on the window.
However, it is claimed there is optimism that the deal will happen and the 22-year-old will head to north London.
Rodon is also standing by to undergo a medical with Tottenham as soon as the two clubs have an agreement in place.
Tottenham missed out on signing a centre-back in the international transfer window, but could add Rodon to the ranks before the domestic window closes.
Swansea are already looking at potential replacements for the Wales international.
They could move to bring in Ryan Bennett if Rodon heads out of the Liberty Stadium exit door.