Modric, 25, expressed his desire to leave Spurs in writing on Wednesday night after weeks of speculation about his future, but Redknapp has moved swiftly to dismiss the request, insisting the club will not be held to ransom over the player.
"We know Luka wants to leave," Redknapp said. "Writing it down on a piece of paper doesn't make much difference to our stance."
Modric has been the subject of interest from Chelsea, who saw a bid of £27 million turned down on Monday, though he landed in South Africa on Thursday with his team-mates for Spurs' pre-season tour.
Chelsea are expected to return with an offer in the region of £30 million for the Croatia playmaker, but Spurs are thought to be holding out for an even higher fee.
Modric has publicly stated his desire to leave for Stamford Bridge and recently slammed the conduct of Daniel Levy, claiming the Spurs chairman had promised he could leave if the Blues offered a sum in the region of £25 million.
Spurs captain Michael Dawson is hopeful that the furore surrounding Modric will not affect the club's pre-season tour.
"The transfer talks happen year in and year out and rumours come and go,'' Dawson said. "All we can do is to concentrate on the job ahead and aim at getting trophies this season.''