The 18-year-old midfielder, who has started eight out of the last nine games for the Baggies, is out of contract in the summer.
Albion have put a long-term offer on the table, but he is yet to sign, sparking fears he could leave on a free transfer at the end of the season.
The Baggies would still be entitled to compensation if that happened, because he is under 23, but they do not want to let him go.
And head coach Darren Moore is confident the talented teenager will commit his future to the club.
"The update I believe is his advisers and our advisers at the club have proposed a deal,” said Moore. “We're one step again closer. We have moved on.
“Obviously it's about Rekeem's advisers and us coming to an agreement. We're getting there.
“We want to see him stay here, we've agreed that we want him to stay, his advisers agree that he should stay, it's just a matter of getting it sorted now.”
Harper has forced his way into a regular starting spot with a number of eye-catching performances, culminating in a versatile display in the derby day victory at Villa Park.
“His ability to soak up the atmosphere was incredible,” added Moore. “He's going to be a top player for us.
“His performances are getting stronger and better. He's shown he has the appetite to cope at this level.”
When Harper was asked if he was going to sign a new contract he said: “I don't really want to talk about that, I'm just trying to focus on my football, keep playing, keep showing the fans what I'm about, keep helping the team win.
"I've been waiting for my opportunity, I felt like I needed to do something to show what I'm about.
“Fortunately I've been given a chance, and I'm just trying to go from strength to strength, just keep playing, progressing and help the team. My focus is just doing my best for the team and the club.”
Supporters are worried Harper could follow former academy stars Tyler Roberts and Izzy Brown out of the door, but Moore insists he’s not fazed.
“I'm not concerned because I feel the right place for him is West Bromwich Albion,” said the head coach.
“Rekeem's a local boy, he's still young and needs his family around him. He's still establishing himself as an elite footballer.
“This is the club to keep him right, we know his strengths and where he needs to improve, and he is improving.
“He's enjoying his football so why change that? His development is here.
“There's still aspects of the game we work on with Rekeem every single day, he's getting stronger. We're developing him and he's coming along really well.
“For him to play in a local derby and put in a performance like he did, is one he and his family can be proud of.
“It's a proud moment to see the academy players on the front line, that's what we intend to do at this club.”