The 32-year-old left-back is set to depart Anfield at the end of the season after nearly 400 appearances in a nine-year span.
Rumours surrounding a potential return to his childhood club, Celtic , were prevalent, but a recent update from transfer journalist Fabrizio Romano appears to end the speculation.
On his X account, Romano announced that the Scotsman and the currently relegation-threatened north London club have spoken about a transfer.
The update stated: "Tottenham have a verbal agreement to sign Andy Robertson in June 2026, all terms in place.
"Nothing signed/sealed yet, as staying in the Premier League will be a key factor ahead of proceeding.
"Robertson, ready to pick #THFC project if relegation battle has a positive outcome."
Spurs appointed Roberto De Zerbi as their manager last week, replacing interim manager Igor Tudor.
Their hopes of remaining in the Premier League suffered another setback on Friday night when Nuno Espirito Santo's West Ham United trounced Wolves 4-0, dropping Spurs into the relegation zone with just over a month of the season to go.
Back in Celtic, there's fierce competition for the first-team left-back spot between Kieran Tierney and Marcelo Saracci, who is on loan from Boca Juniors.
As per a report last month from Saracci's agent, the club is in negotiations with the 27-year-old Uruguayan regarding a permanent move to Scotland this summer.