The Gunners were still involved in three competitions this time last week, but were knocked out of the FA Cup by Watford on Sunday, before Barcelona put them out of the Champions League misery at the Nou Camp on Wednesday.
On the plus side it allows Arsene Wenger's side, who are third in the standings behind Leicester and Tottenham, to focus all their attention on overtaking the Foxes at the top of the Premier League - though looking at their fixtures Redknapp believes the winner will come from the current top two.
Speaking on talkSPORT's Alan Brazil Sports Breakfast show on Thursday, the former Spurs boss said: "They (Arsenal) have got tough games, they’ll do well to win at Everton. They’ve got to go to West Ham as well - they’ll do well to win at West Ham. They can’t afford to lose any games."
Previously, Redknapp told the Telegraph that Leicester would finish the season as Champions, but is now offering hope to his former employers as well.
"It’s going to be tough (for Arsenal) - I think the winner will come from Leicester or Tottenham."
Arsenal have a game in hand on their title rivals, but are 11 and six points behind them respectively.
As well as their trips to Everton and West Ham in the coming weeks, the Gunners face fourth-placed Manchester City at the Etihad Stadium on the campaign's penultimate weekend.
Leicester have never won English football's top division, while Tottenham have managed it on just two previous occasions.