The former Spurs boss has signed three players so far this summer: goalkeeper David Stockdale, defender Marc Roberts and midfielder Cheick N'Doye, though he insists that further additions are needed.
The 70-year-old told 'BBC WM': "We're a little bit short at the moment - we need to improve the squad this week if we can.
"We've been trying, but it's been very difficult to get the players in who we've been chasing. Hopefully we'll get there - it's not been through lack of effort."
Redknapp is believed to be interested in signing Middlesbrough midfielder Stewart Downing, though it appears that the move has been complicated by the player's wage situation. 'Brum' are said to be unwilling to match the player's current wages, whilst 'Boro' are unwilling to pay a portion of the player's waged for the remainder of his contract in order to push through a move.
Another player on Redknapp's wishlist is Bristol City defender Aden Flint.
"I like him (Flint) but we'll only pay what we can - if he's too expensive then we'll move on," the Birmingham boss explained.
Meanwhile Brimingham defender Ryan Shotton could be edging closer to leaving the club, Redknapp confirmed at the weekend that there had been a bid for the player and that Shotton wanted to move though the interested party is as of yet unnamed.
There was, however, speculation earlier in the summer linking Middlesbrough with a move for the former Stoke man.