Richardson, 26, is out of contract at the end of the 2010-11 season and Sunderland are keen to retain the services of a player who can function in both defence and midfield.
"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."
Sunderland are also reluctant to allow Martyn Waghorn to leave the club on loan this season, dashing the hopes Hull City had of securing the young striker.
"The kid was outstanding on loan last season and now I think that 70% of the Championship would like to take him," Bruce told the Hull Daily Mail.
"I have said that his future is with us this year and nothing has changed. I wouldn't have thought I would be loaning him out this season."