A spokesman for the corporation said he had undergone surgery for a heart problem but had no further details.
The Daily Record reported that he had been suffering from a virus.
Relatives of the 51-year-old, who also played for German club Borussia Dortmund and Hibernian, were understood to have been at his bedside.
MacLeod won 20 Scotland caps and played at the 1990 World Cup in Italy.
He played for Celtic between 1978 and 1987 before moving to Germany. He captained Hibs to a League Cup win in 1991.
In 1997, he became Wim Jansen's assistant manager at Celtic and helped them win the league in his only season in the job.
Since then he has been a football commentator on BBC Radio Scotland and BBC TV.