After considering an offer worth £5m from Spurs for Robertson, Liverpool decided to pull the plug on the deal despite the Scottish star being out of contract once the season ends.
The Reds were debating whether to get Kostas Tsimikas back from loan at Roma as a replacement for Robertson, but he is not deemed good enough to step in for the 31-year-old who still plays a huge role in the side.
Both Conor Bradley and Giovanni Leoni are out for the season, leaving head coach Arne Slot with a severely depleted back-line which has also impacted the decision to keep Robertson until his contract runs out.
However, as reported by talkSPORT, the Reds would be willing to sell if a strong replacement is brought in during the final days of the winter transfer window.
The report states that Liverpool and Robertson are understood to be relaxed about the situation and the club are keen to let him have a proper goodbye to supporters after several years of service which has seen him win every trophy possible under both Arne Slot and Jurgen Klopp.
Robertson remains a professional figure in the dressing room and is one of the most experienced players in the side under Slot who values him greatly.
Following an injury to Ben Davies, Tottenham are heavily on Destiny Udogie as they search for a quick fix this January.