The 26-year-old has less than 12 months left on his current contract but Bruce is thought to have made a breakthrough in talks to tie him down on a long-term basis.
Negotiations have progressed over the duration of the summer, but despite not playing in the club's 4-2 win over Hull on Saturday, Bruce was confident that Richardson will commit his future.
"We're talking to Kieran, he's got a year left and we hope we can tie him up," Bruce told The Journal.
"I think the chairman has made a few inroads into that.
"We hope he signs it. We want to build a squad here and Kieran is a very good player. They have always got you by the short and curlies these players because he has only got a year left.
"We hope it will get done and we hope we'll be able to announce something shortly. I like him as a player. He has got a bit of versatility and he can play in a number of different positions.
"In my mind, I think his best position is left-back. I've always said that, but he is a good player and it's nice to have different options with him in the squad."