Amid suggestions Spurs hold a buyback clause for their former star, the current manager is open to a reunion
The transfer agreement between the two teams was leaked online on Wednesday and appeared to show that Madrid paid a world-record €101 million and revealed the Premier League club's option to match any offers received for him before 2019.
Bale, who has 13 goals and nine assists to his name this season, has spoken in the past of a potential return to the ground where he first rose to prominence and Pochettino is open to the possibility.
"I don't know – it's about rumour," the Tottenham manager said of the clause. "If we have the full option to sign him then why not?
"He's a great player and he's a player who can improve our squad. This is the type of profile we [try to] find."
READ MORE | How Spurs could BLOCK Man Utd move for Bale
Spurs have been linked with reigniting their summer interest in Saido Berahino during the January transfer window, while Barcelona forward Sandro Ramirez has been added to the growing list of reported targets.
He added: "There are a lot of rumours and names, but my position is always to respect the clubs, their names and the players. I never speak in public because respect is very important to show for clubs and the players."
Emmanuel Adebayor - whose Spurs contract was mutually terminated in September - has been linked with Palace, whose manager Alan Pardew confirmed he was a target in the current window.
But Pochettino refused to comment on the striker, adding: "It's not my problem. I think that I cannot give an opinion about Adebayor or Crystal Palace.
"I respect him and Crystal Palace and what is happening at different clubs is not my problem."