The 31-year-old’s return would mean a second spell in English football, Keller having previously played for Millwall and Leicester between 1991 and 1999. He then headed to Rayo Vallecano and was released earlier this summer.
Director of football David Pleat confirmed: "He’s having medical today with a view to agreeing a deal to come back from Spain to join Tottenham."
Keller's agent, Colin Poundford, was earlier quoted as saying: "After several offers that the player has received this summer, from many teams including Besiktas, Tottenham and another important English side, Keller has decided to sign for Tottenham Hotspur.
"He had his medical yesterday and early this morning. I have not spoken to the player or to the club in order to know when he will be officially presented. Tottenham are away at the moment in Greece, but are returning this evening."
American international goalkeeper Kasey Keller is undergoing a medical ahead of a proposed move to Spurs from Rayo Vallecano.