Manchester United were in pursuit of the 23-year-old during the transfer window.
Jose Mourinho was believed to have identified Dier as his first-choice holding midfield target.
But United found Spurs difficult to do business with as they ultimately signed Nemanja Matic from Chelsea for £40m.
The Serbia international’s reunion with Mourinho has gone well so far, but Dier was the preferred choice.
Ex-Tottenham team-mate suggested Dier was keen on the move last week.
The pair are on international duty with England, and when Dier jokingly called the Manchester City defender a ‘traitor’ for leaving Spurs, Walker replied in an Instagram video: “It was alright when you wanted to go to United.”
When questioned about the circumstances surrounding his future, though, Dier said: "I think it’s best if footballers worry about playing football.
"I take the philosophy that if I worry about the football everything else will take care of itself."
With Dier insisting his future did not concern him amid the summer speculation, he is now focused on Tottenham and England.
Manchester United could return for Dier in the future, though, with 29-year-old Matic not necessarily viewed as a long-term solution.
Meanwhile, the versatile Spurs star could return to England’s starting XI for their crunch World Cup qualifier tonight at Wembley against Slovakia.
