The north London side are aiming to be one of the main teams challenging for a top-four finish this term after they ended up in sixth place in the table under Arsene Wenger last term.
The Gunners have made something of a slow start to the new season under new manager Unai Emery, with Arsenal having only won one of their opening three Premier League games so far.
Arsenal picked up their first Premier League points of the season last weekend when they claimed a 3-1 win over West Ham United at The Emirates.
Emery has been tasked with steering Arsenal back into the Champions League qualification spots this term, with the Gunners having missed out on a spot in the top four for the last two seasons running under Wenger.
However, Redknapp feels that finishing in the top four is likely to be a stretch too far for this Arsenal side this season.
Speaking to Sky Sports, Redknapp said: “I don’t think any manager could [get this team into the top four], not at the moment.
“I just think it is going to take time. Arsenal have been falling further and further behind and I think Arsene Wenger has left Unai Emery with a badly-balanced squad with not enough quality in it.
“It’s as simple as that. I don’t care who the manager is – Pep Guardiola or whoever – it is going to take time and he needs it.”
Arsenal will look to make it back to back wins in the Premier League on Sunday afternoon when they travel to Cardiff City in the top flight.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news