The rugby league commentator had been the subject of complaints by five women at the corporation, including claims of groping, according to the Sunday Times.
Riley did not cover the Rugby League World Cup match between Wales and Papua New Guinea on Saturday.
He has been a presenter of 5 live Breakfast since 2011. He also presents darts and snooker for BBC television and radio
The paper said the conduct of another unnamed BBC employee has also been raised as it emerged some of the BBC’s most senior female presenters has formed a group to “discuss issues” and “offer support and advice” to female colleagues.
Presenter Mishal Husain and TV broadcaster Victoria Derbyshire are reportedly among the women behind the group.
A source said: “Complaints about these two men may just be the tip of the iceberg at the BBC.
“This group is formed from some of the BBC’s most powerful female talent and editors. It will not stand for sexual harassment of women at the corporation.”
The Sunday Times said the group came about after the row about the BBC gender pay gap in the summer, but since the Harvey Weinstein Scandal has turned its attention to sexual harassment.
Husain responded to the article on Twitter, saying it was “an inaccurate portrayal of conversations women at the BBC have been having”.
She added that the group “discusses a wide range of issues, offering support and advice where necessary, it is wrong to portray it as being focused on sexual harassment or targeting individuals”.
The BBC will make a decision over Riley’s future after an inquiry into the allegations, it was reported.
A BBC spokesman said “We can’t comment on individuals but treat any allegations seriously and have processes in place for investigating them.”