Drogba has snubbed the offer of a one-year contract extension by Chelsea, and is believed to be looking for a big-money move away from Stamford Bridge.
With the arrival of £50 million signing Fernando Torres in January and the emergence of Daniel Sturridge, Drogba is no longer guaranteed a place in Chelsea's starting XI. And Redknapp, who has also admitted his interest in Drogba's strike partner Nicolas Anelka, admitted he would be keen to bring the Ivory Coast international to White Hart Lane.
"Drogba is a top player, a fantastic player, so, who knows? I couldn't sit here and say we wouldn't be interested," Redknapp said. "Anyone would be interested in having Didier Drogba in their team but we have not made any enquiries."
However, it appears Drogba would not be guaranteed a starting berth at Spurs, with Redknapp admitting to a selection headache following the return of Rafael van der Vaart from a hamstring injury.
On-loan striker Emmanuel Adebayor has been in impressive form for Spurs, while Jermain Defoe scored in Tottenham's win over West Brom last weekend.
"It's a difficult decision," Redknapp said. "Rafa is available but Jermain scored a good goal last week. Both of them are outstanding and neither deserve to be left out of the team."