Redfearn was appointed in November last year on a 12-month rolling contract and agreed with owner Massimo Cellino at the time that he would revert back to academy boss if it did not work out.
But he has steered Leeds away from relegation danger after five wins in seven matches and believes he will be in place beyond the end of the current campaign.
"I'm hoping so. I think I've done enough if I'm honest," Redfearn said. "But there's still a long way to go (this season) so I don't want to tempt fate or pre-empt anything because we want to finish well regardless. We want to do well for the club.
"I've got to start thinking that way and to accept that I'm going to be here. I've got to make sure we've got the right blend, the right system and the right way of playing so we can hit the ground running next season.
"I've spoken to (Umbers) about the fact that we're a little bit light. We're a bit unbalanced. Since the turn of the year, seven players have gone out and three have come in and one of the three came in injured."
That player is midfielder Granddi Ngoyi, who has yet to appear for Leeds following his arrival on loan from Palermo due to a thigh injury.
Redfearn added: "It's a big turnover and when you come to this time of season, you get a raft of games and your squad can get stretched. And what I don't want is for this season to fizzle out. I want to finish on a strong run.
"We've been talking about players for next season, who we're going to keep and planning pre-season, but nothing official has been announced.
"But I get on with it as I'm told to get on with it. Players here have put in a lot of effort and have really bought into what we're doing. I've got the backing of the players, they love what they're doing and they've got a clear sight of where they're going. We want to continue that."