Hungary international Kerkez would be the only senior left-back for Slot to call on if Robertson is sold, but Liverpool could look to recall Kostas Tsimikas from his loan spell at Roma.
Tottenham completed the signing of Brazilian left-back Souza on Thursday and are already well stocked in that area of the field.
Destiny Udogie has been the preferred choice of manager Thomas Frank this season, with Djed Spence also offering cover.
Ben Davies was another option, but the Wales international sustained a broken ankle on Sunday and has been ruled out for the rest of the season.
Spurs’ move for Robertson could be a bid to add experience to a young squad, with 32-year-old Davies the only player over the age of 30.
Robertson has won nine trophies during his time at Liverpool, including two Premier League titles and the Champions League.