Spurs are third going into the weekend action, with Redknapp upbeat about the prospects for the coming months.
He told reporters: "The top four is a target, a difficult target to achieve, but it's where we want to be and where we want to aim for.
"We've got to believe we can get there and we will keep trying as hard as possible. We'll give it everything we've got and there is no reason why we can't achieve it with the squad we've got. I think we can do it."
Meanwhile, Redknapp has backed Mexico striker Giovani dos Santos to make his mark as he nears a full recovery from an ankle injury.
He added: "I'm looking forward to getting him back fit, he's a good young player and was in great form before he got injured. It was a big blow for us to lose him at that time.
"I want him to stay and there is no chance he'll be leaving. I want him to do what we hope he can do - be a big player for Tottenham."
Redknapp also confirmed that Spurs are closing in on a deal to sign defensive midfielder Sandro from Brazilian club Internacional.