Nelsen, 35, has been linked in recent days with a coaching role at former club DC United in the United States and Redknapp admitted there was substance in the speculation.
Redknapp said: "There is some truth in the rumour I'm afraid. Nelsen is very important to us, a fantastic leader, a top player. But he has been offered a job in America and I think there is every chance he might want to go.
"He wants to be a manager and it is a chance for him to manage a club.
"He has been fantastic. I took him to Tottenham last year from Blackburn. He's one of the best pros I've ever met in my life, a fantastic player, a great trainer, a leader. He is a massive part of your team. To lose him would be a massive blow for us."
Nelsen is in the middle of a one-year contract but Redknapp said: "I'll have to speak to the owner to see what the situation is with that. We'll try (to keep him) but it is difficult."