"If I had said we were going to finish fifth in the Premier League a couple of years ago, you would all have thought I would end up in the nuthouse, wouldn't you? But there is a chance," Redknapp declared. "It would be great if we can do it, but let's see how we go.
"At the moment, it looks as though there's only going to be one UEFA Cup spot in the league for the team who finish fifth, so it is going to be very tight.
"There is a whole group of us in there scrapping - we have all done well and we are all in there in that top group."
Redknapp, whose side have won their last two league games, maintains it will be some achievement to have been in the hunt, never mind where they finally end up.
"Every year you finish in the top half of the Premier League table you are doing absolute miracles," Redknapp said on the club's official website.
"Let's hope we can have two years running finishing in the top half. It would be a great achievement.
"We are a good team and I think people give us respect.
"We have got to be aiming to have a really good run between now and the end of the season - and if we qualify for Europe, then great."