Less than a week ago, Redknapp claimed he would not be doing any business this month but has since seen midfielder Sandro and central defender William Gallas join the club's injury list. Several of the papers on Friday morning have hinted at a double swoop on Blackburn for Chris Samba and Junior Hoillet.
With Spurs now just six points adrift of leaders Manchester City and three behind Manchester United with a game in hand on both clubs, the White Hart Lane side are firmly in the title hunt going into the second half of the season.
Redknapp believes that the addition of a brace high-quality signings could help them push the Manchester duo all the way, but admits it will be tough to find available players to bolster his current squad.
"If you'd told me six months ago that my Spurs side would be right in the mix for the title, I'd have laughed," the veteran tactician wrote in his column in The Sun.
"And if we could find a couple of new faces to improve us even further over the next month, then who knows where this season could take us?
"The problem we have now when we look for players is that the better you get, the more difficult it is to find someone who will take you even higher.
"Believe me, there aren't that many out there - but we won't fall down on that score through a lack of looking.
"I'm not about to say the Premier League is coming to Tottenham because there are still so many who could have a big say.
"And it doesn't take a genius to point out that Manchester City are still red-hot favourites, while anyone ready to write off United needs their head looking at."
Redknapp has held a long-term interest in Trotters defender Cahill, but the England international looks certain to leave the Reebok Stadium for Chelsea in the coming days.
Bolton have agreed a fee with their Premier League rivals, however, with the Blues and the 26-year-old haggling over personal terms, there had been suggestions other clubs could step into the breach.
Yet Bolton boss Owen Coyle still expects his key defender to depart for West London, particularly as Spurs were more interested in a player-exchange deal.
Coyle said: "Tottenham have always been admirers. But they are more interested in swapping players. We could probably never afford their salaries.
"We have agreed a fee with Chelsea and we honour our word."
