Spurs boss Pochettino remains a target for Manchester United, according to reports.
Pochettino has continued to impress as manager of the north London club, taking Spurs to third in the Premier League table and just five points behind both Liverpool and Manchester City.
He has managed that despite being on a shoe string budget, with Spurs having to spend more and more on their new stadium - of which they are yet to relocate to from Wembley.
Former Spurs midfielder Brown delivered his verdict on keeping Pochettino, hoping he remains at Spurs and turn them into an even bigger club with the help of their new stadium.
"He will be highly sought after I'm sure," Brown said. "Manchester United will still be looking at him. It would be such a shame to start all that again for the Spurs supporters going into this new stadium.
"I think he can take that club to the next level, by making them stronger and stronger in their new stadium."
Pochettino signed a new contract at Tottenham last May, which sees him remain at Spurs until the summer of 2023. He is currently earning an enormous £163,000 a week (Guardian).
The Argentine manager's focus will be on Wednesday night, rather than potentially taking over at Old Trafford, as Spurs play host to Borussia Dortmund in the last 16 of the Champions League.