The ex-England captain spoke to Dan Walker.
The former England captain remains on contract with the organisation, and they expect to work with him in the future.
Azeem Rafiq claimed that he made a racist remark to a group of Asian players.
He will not be involved in the coverage of the Ashes in Australia.
"We're in regular contact with Michael," the statement said.
We have had positive conversations with him.
In 2003 and 2008, he was the captain of England. He was a summariser on the Test Match Special in 2009, after playing his entire domestic career at Yorkshire.
He denied the claim in a recent interview with the BBC, but admitted to sending some racist messages in the past.
Rafiq had gone through a lot during the Yorkshire racism scandal.
Rafiq said that during a County Championship match for Yorkshire in 2009, he and three other Asian players were told "too many of you lot, we need to do something about it".
Rafiq's account was supported by Rana Naved-ul-Hasan and Adil Rashid, who both said they heard the comment.
The fourth player in the group, bowler Ajmal Shahzad, told the Daily Mail that the senior guys were good to him.
"Our contributors are required to talk about relevant issues, so Michael's involvement in a story of such significance means it's not possible for him to be part of our cricket coverage at the moment," said the BBC.
We're happy with how our conversations are going and we're looking forward to working with Michael again in the future. He is on a contract with the BBC.
