Pochettino guided Spurs to a fifth placed finish in his first season in charge, and helped to bring through a number of young players during that time.
The start of this campaign has not gone according to plan, though, with Spurs being able to collect just one win from their opening five matches - but Redknapp feels that Pochettino still has time to make an impact, before anyone will be thinking about firing him.
"I don’t think Pochettino is under any real pressure just yet," he said in the Evening Standard. "His aim is for Tottenham to make the top four but I’m sure he wants to win a competition. He showed that last season."
Pochettino has had to work under limitations so far during his time at Spurs, due to the failed recruitment of his predecessors.
Spurs have had to amend their transfer plans, due to the amount of expensive, unsuccessful deals they have completed in recent times.
As a result, Pochettino has been forced to find new ways to improve the squad, and his main policy has been to bring through players from the youth academy.
The likes of Nabil Bentaleb, Ryan Mason and Harry Kane have all thrived under Pochettino's leadership so far, and it seems as if Spurs are planning for the long-term under the Argentine's stewardship.