The 22-year-old England international on Monday completed a £5.5million move from Manchester United to Sunderland after his former team-mate persuaded him his future lay away from Old Trafford.
Richardson's opportunities at United, where he emerged through the ranks, were limited as the likes of Ryan Giggs, Cristiano Ronaldo and Paul Scholes kept him on the sidelines for long periods last season.
However, Keane believes he has untapped potential and is confident he can get the best out of him at the Stadium of Light.
The Irishman said: "Kieran is just a young lad, he has had some good moments in his career playing for England and having success with United.
"But my job as a manager is to get more out of players and keep pushing them.
"Hopefully Kieran's decision to come here means he feels we can maybe push him on.
"You are always pushing players to keep getting better.
"For an attack-minded player like Kieran, it is very difficult at a club like Man United, there is no getting away from that."
Keane added: "United will always bring in players, they will always buy players and especially attack-minded players, because that's what the club demands and that's what the fans demand.
"When you come up through the ranks like Kieran, it can be difficult. But he has contributed to United's success over the last few years.
"He played his part in winning the league last year, so hopefully he can play a big part for us."
Richardson forced his way into the England squad after producing a fine run of form on loan at West Brom in 2005, but could not hold down a regular place on his return to Old Trafford.
The chance to play week in, week out at Sunderland proved hugely attractive, although the knowledge that a man he admires so much wanted him in his team clinched the deal.
Richardson, who like fellow new arrival Michael Chopra will not make his debut at Darlington on Wednesday night, said: "He is so passionate about his football and I love that.
"I am passionate about my football and when someone like that gets behind you, you feel you go out there representing him and you want to show him what you can do and do well for Sunderland.
"He just told me he wanted me at Sunderland. He felt he could get the best out of me, and when someone like that of great stature says that to you, you listen to him because he was probably the best midfielder in the world.
"When a man like that wants you, you feel obliged."