Richardson has just a year to run on his present contract and Black Cats boss Steve Bruce is keen to tie him down to a new long-term deal.
The 25-year-old midfielder impressed at left-back last season and Bruce admits his versatility makes him a key member of his squad.
"Niall (Quinn) has had talks with Kieran's father," Bruce told the Northern Echo. "And they're ongoing.
"I was delighted with Kieran last season, and the way he played at left-back.
"I think he's got his head around it now (playing at left-back) and he's OK. But of course he also can play in midfield and I'm not ruling that out. He's another player we have who can play in midfield."