Premier League - Spurs ignore Modric request
It is claimed Modric took the step on the same day that he flew out with his team-mates for the club's pre-season tour to South Africa.
Modric, 25, has made clear he wants to join Chelsea this summer but Tottenham have rejected two offers from their London rivals, believed to be worth £22 million and £27 million.
Initially the Croatia midfielder said he would not hand in a transfer request but Tottenham's refusal to negotiate with Chelsea has forced his hand.
Modric claims he has a "gentleman's agreement" with Daniel Levy that would allow him to discuss a move to a bigger club, and has criticised the Spurs chairman for failing to follow through with his promises.
However, both Levy and manager Redknapp remain adamant that Modric will not be allowed to move to Stamford Bridge.
Redknapp says he does not know whether Modric has requested a transfer, but Spurs' stance remains unchanged in any case.
"We know he wants to leave, whether he writes it down on a piece of paper doesn't really make any difference to our stance," he told BBC Sport.
"He's a great player and we don't want to lose him."
Defender Michael Dawson told Sky Sports News: "This time of year there are always going to be rumours and Luka's been linked with Chelsea.
"From a team's point of view you want to keep your best players and the chairman has come out and said he is going to keep him so that is great for the football club.
"We are all friends with Luka, we have got great team spirit amongst the players and we want to keep that together. The chairman has come out and said no one is for sale so that's great."