Szczesny has sought to step up the mind games between his team and their bitter rivals as the fight for a Champions League spot intensifies. The 21-year-old had a dig at Spurs after the Gunners' 3-0 win over AC Milan, claiming Redknapp's team may be playing Europa League football next year - something he said would give him great pleasure.
His outspoken attacks may have made him a cult hero among Arsenal fans, but Redknapp is not impressed. He said: "Szczesny says he is coming to get Tottenham? Oh yeah, yeah, he does have a lot to say Szczesny, doesn't he?"
He added:"I'm a big fan of his, he is a fantastic goalkeeper and he could end up being one of the best goalkeepers in the Premier League but he does come out with some stuff doesn't he? He was having a go at Chelsea the other day and god knows what (else)...
"He is a fantastic goalie, but he should just keep doing what he does."
The Polish keeper also rounded on Chelsea, who trail Spurs by four points, claiming the reason why Blues owner Roman Abramovich has sacked so many managers is because a group of senior players practically run the west London club.
The sniping between rival clubs is, of course, a key reason why the Barclays Premier League is seen as one of, if not the best, domestic competitions in the world, and Szczesny's verbal salvo is unlikely to be the last between the two clubs this season.
But Redknapp is not a big fan of players attacking other clubs through the media.
"I don't like it," he said. "There is no need for it. Just get on with it, just get on playing.
"You weren't allowed to speak to the Press when I was playing. If you got caught you got a fine of a week's wages, which was about £7."