The vastly-experienced coach believes Arsene Wenger's side are closer than ever to winning the Premier League title.
The Gunners are being touted as potential Premier League title challengers after impressing over the second half of last season.
There is a belief that they will be there or thereabouts after they lured goalkeeper Petr Cech away from reigning champions Chelsea, with many believing that he could be the player they have been missing for so many years.
Redknapp, though, thinks it is two English stars that will have a crucial role to play in Arsene Wenger's plans.
“It’s going to be tight this year but I’ve got a feeling for Arsenal,” he told talkSport.
“I’ve just got a feeling Arsenal might come strong this year, if Arsene [Wenger] keeps his players fit, people like [Jack] Wilshere and [Theo] Walcott. Last year they weren’t far away and had lots of injures and lost key players. This year they could go close.”
Closer than ever before but one more addition is necessary
While it is yet to be seen if Arsenal can win the title next season, it is safe to say that they are very much in the mix.
Securing Cech was a big step in the right direction as it has strengthened arguably their weakest area, with David Ospina a solid deputy as well. They also have a wealth of options in other departments, with their defence, midfield and attack loaded with high-quality competition for places.
Despite that, there are still lingering doubts over Olivier Giroud and his ability to score the requisite number of goals. Perhaps if the Gunners were to add another forward during this window, then a title challenge would be even closer.