Walker is aware that Manchester City are prepared to double his £70,000 a week salary if they sign him. It is believed Spurs are willing to listen to offers for the England defender.
Pressed repeatedly on Walker’s situation, Pochettino said: “There are a lot of rumours. I never speak about rumours.”
Asked if the 26-year-old was happy, Pochettino replied: “I cannot confirm this. They are rumours. If I speak about all rumours, it would be a two-our press conference. It is about football.
“Tottenham are the team most involved in the rumours. You see now that with still two weeks of the season to go, there are many rumours. It does not affect me.
"I am so calm and the players are very calm. We will see at the end of the season whether or not the rumours are true.”
Standard Sport revealed last Monday that Walker held talks with Pochettino about his future.
Kieran Trippier was preferred at right-back in both the FA Cup semi-final defeat by Chelsea and the 2-0 win over Arsenal, but Pochettino denied this was a snub to Walker, who his manager said had trained as normal this week
He said: “We will decide which players will leave, who will stay and who we sign. The games against Crystal Palace and Swansea [which Walker started] were also big.
“Whatever happens to any of our players will be a club decision. I am Tottenham manager but this is not Mauricio Pochettino Football Club. That is very important to clarify.”
Pochettino, chairman Daniel Levy and head of coaching John McDermott make up the three-man football committee, to which chief scout Steve Hitchen reports.