Potts is regarded as good prospect at West Ham, but his lack of first-team opportunity over recent seasons has given Luton cause for optimism.
The League Two side believe that they could capture the full-back and it would be a signal of their intent if they did.
Luton will be hunting a promotion place this season, as one of the biggest clubs in England's fourth tier, and they seemingly feel Potts could be a vital piece of the jigsaw.
A full-back who is capable going forward as well as doing a solid job defensively, Potts has already impressed in League Two - on loan spells earlier in his career - and he will be hoping to show his class again if he does move on.
West Ham may be reluctant to sell him, though, unless they are able to secure the singing of a right-back in the summer.
Carl Jenkinson has finished his loan spell at the Boleyn Ground, meaning that the Hammers are currently short of cover in that position.