A spokesman for Championship club Birmingham, who gave Francis his professional debut in 1971, said they had been informed by a person close to the former player's family that he had been taken ill on Friday.
It is believed Francis was taken to Solihull Hospital and the spokesman said they had been told that the 57-year-old had had a stent (tube) fitted and was making a good recovery.
Francis played for Birmingham between 1971 and 1979 and became the first player in English football to cost a £1million fee when he joined Brian Clough's Forest.
He repaid that fee by scoring the winning goal in the 1979 European Cup final against Malmo.
Francis won 52 caps for England and also had spells at Manchester City, Sampdoria, Atalanta, Glasgow Rangers, QPR and Sheffield Wednesday.
He returned to boss Birmingham between 1996 and 2001 after previously managing QPR and Sheffield Wednesday and has been out of the game since leaving Crystal Palace in 2003.
A statement on Birmingham's official website read: "Everybody at Birmingham City FC would like to send our best wishes to club legend Trevor Francis following news that he is recovering in hospital from a suspected heart attack.
"The former Blues striker and manager is much loved by everybody associated with the club and we'd like to wish Trevor a speedy recovery."