Spurs want to land Rodon before the transfer window shuts, but started from a position of valuing him at £7m, while Swansea believed he was worth £20m.
Talks between the clubs have now seen the distance between themselves narrow significantly, although there is still a gap.
Spurs are prepared to go up to £10m to take Rodon to north London, but Swansea want around £15m.
With just hours to go before the clock stops ticking, Tottenham and Swansea are still £5m apart in their valuations of the 22-year-old defender.
The two clubs are currently engaged in discussions as they look to reach an agreement over a deal for Rodon in the final hours of the window.
If Tottenham can agree a transfer fee with Swansea, agreeing personal terms with the centre-back would only be a formality, with the player keen on the move.
It remains to be seen if Tottenham can win the race against time and strike a deal to sign Rodon from Swansea.