Trippier had texted Pochettino after his departure from Spurs, but the right-back never got a message back from the Argentine.
And Kane mentioning about Trippier trying to get in contact with him was the first that Pochettino had heard about the message.
"I didn't see [the quotes from Trippier] but I heard about it,” Pochettino said.
“I can explain how I feel. We had a conversation where he explained he was going to move to Atletico Madrid - okay nothing more.
"Yesterday when Harry Kane arrived back he said to me did you get Kieran’s text? I said 'no' because I changed my number. Maybe because he doesn't have the new number?
"He believes his words were twisted - I don’t know anything more. Kieran translated this message to me through Harry Kane. He wanted to tell me.
"But I've got no problem with Kieran.”
Trippier has been fairly outspoken since leaving Tottenham, and even suggested recently that they got rid of him too early.
The right-back may have been proven correct so far this season, as Spurs have struggled to find a consistent performer on the right hand side of their defence.
With injuries mounting up, Davinson Sanchez was required to play at right-back in Tottenham’s last game against Arsenal and badly struggled.
Trippier’s form was poor in his last season at Spurs, but he would arguably be an upgrade on what Pochettino has available in the position currently, especially with Juan Foyth still sidelined.
Spurs are next in action tomorrow, when they take on Crystal Palace.
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