The Icelandic international is 32 in December and played 11 times for Monaco in the French League without finding the net.
But Redknapp said: "Listen we've taken him till the end of the season. It's not a long-term but a short-term loan. If Eidur comes in and does well we can look at next year, it's up to him. It's a good deal I think you'll find from our point of view.
"He might as well have stayed at Monaco, which is not the worst place to be is it? I suppose. But he wanted to come here and play. He wants to play football.
"He had a great spell playing three in midfield, as an attacking midfield player. He can play off the front at the point of a diamond, he's played off the wide positions at times. He's not a winger but coming off the wide positions.
“It's all competition for places. Eidur can play and it gives me options to play differently. "If Aaron Lennon's not fit and I've got no real width we could play with diamond. I could play different systems with him. He's a good player to have around. Hopefully he'll be of use to us and do well.
"I don't think the other players will take it the wrong way. But it keeps them on their toes. They've got to do well to stay in the team. It's up to them."