Tottenham also face German side Borrusia Dortmund in the last 16, first-leg of the Europa League on Thursday and Walker wants Spurs to hold on to the Argentine, whose achievements have not gone unnoticed by their rivals.
"It is vital," the full back told Standard Sport.
"We've built a foundation now. We don't need managers coming and going. He did well at Southampton and he's come here and done well so he's proved he's a very good manager."
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Pochettino's organisational skills and demanding training sessions have played a huge part in the team's charge for the title, Walker said, while pointing to the strength of the bond between players and manager.
"He is a very good man-manager," Walker added. "He knows what goes on in your head if you don't play as much as you want to, and I think everyone in the squad feels equal.
"He doesn't concentrate just on the 11 players who are playing and talk only to them. He's the same with the whole squad, so everyone feels welcome and part of the team."
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
