Spurs have won just three of their opening 11 games and suffered heavy defeats to Bayern Munich and Brighton before the international break.
Tottenham’s form has shocked Redknapp, who thought his old club would challenge Manchester City and Liverpool for the Premier League title prior to the 2019/20 campaign.
When asked whether Tottenham could part ways with Pochettino, the former Spurs boss told the Daily Mail: “Yeah, absolutely, that is not going to happen.
“I don’t know if they’ve overachieved. They should be finishing in the top three with that squad, that’s where they should be, there’s no doubt about that in my opinion.
“But to get to a Champions League final was great for them. It was great to see them reach the final.
“At the start of the year I really thought Spurs would push Man City and Liverpool a lot, lot closer. Tottenham have got a great team, with Harry Kane, Dele Alli, [Heung-min] Son – I thought this could be their year.
“But it’s been a disappointing start for them for sure and they need to turn it around quickly, but I still think they’ll finish third.”
Tottenham’s summer and start to the season appeared to be disrupted by transfer talk linking Christian Eriksen, Danny Rose, Jan Vertonghen and Toby Alderweireld with moves away from the club.
A week before their 7-2 home defeat to Bayern Munich, Spurs were knocked out of the Carabao Cup by League Two minnows Colchester.
A second-string team was fielded against Colchester, but Redknapp, who bossed Spurs between 2008 and 2012, believes Pochettino has as good a squad as Manchester City and Liverpool.
He said: “They’ve got a great group of players. It’s some squad, if you go through it, I don’t care what anybody says, I don’t think there’s a lot between that squad and Liverpool’s and Man City’s squad, I really don’t.