The 35-year-old has been appointed head coach of Toronto FC and the Major League Soccer club expect him to start work on February 1, ensuring Tuesday's Barclays Premier League clash with Manchester City will be his final game for Rangers.
Redknapp expected to keep the player until the latter stages of their relegation battle but he is resigned to losing him far sooner, and he said: "I need to speak to Ryan, I need him here for the Norwich game. I thought we were talking March 1 when I spoke to Ryan last. Suddenly this has all changed. I'm hoping we can put it back a few days."
Redknapp, who revealed Nelsen will be rested for Saturday's FA Cup tie against MK Dons, added: "He's been away all week in Canada doing some work for his new club. I need him next week - we're desperately short and I need Ryan to play. He's got a job to go to and wants to crack on with that.
"He felt it's an opportunity that may never come along for him again. I can understand where he's coming from because it's his future, but I wish he was staying because there haven't been too many better players than him here this year."
Striker Loic Remy and defender Tal Ben Haim have been the only arrivals during an otherwise frustrating transfer window that has seen Redknapp miss out on several targets.
Porto defender Rolando is currently on Redknapp's radar, while a deal for Chunnam Dragons' South Korean international Yun Suk-young is close to being completed, but neither goalkeeper Julio Cesar nor centre-back Anton Ferdinand will be leaving.
"I've been travelling all over the place, it's been busy. It's difficult. I've taken lots of flights but it's been very hard to actually land anyone," Redknapp said.
"I've been around Europe every day and haven't been home for 12 days. My wife said to me the other day 'I've forgotten what you look like'. I told her I look like Paul Newman, she said 'in your dreams'!
"You think you've got someone and then something else happens and you don't get the player. I'm chasing here, chasing there, and coming up with nothing. That's how it's been for the last few weeks and the clock's ticking down now. If we don't get the people I want and a bit of quality, we'll sit tight."