Francis is in a stable condition in Birmingham Heartlands Hospital after undergoing surgery and could be well enough to return home within the next week.
A statement from the club read: "The Blues legend suffered a heart attack yesterday and underwent an operation at Heartlands Hospital. Thankfully the former striker and manager is recovering well and should be able to return home within the next week."
The statement continued: "Trevor's family have informed the club that he has been touched by the incredible amount of support that Bluenoses have shown since hearing the news that the 57-year-old had been taken ill.
"They have also expressed a big thank you to Heartlands Hospital."
A spokesperson for the hospital confirmed Francis' condition was stable.
Francis starred for Birmingham from 1970 to 1979 before becoming Britain's first £1million player when he joined Nottingham Forest. He later managed the St Andrews outfit between 1996 and 2001.
Francis has also received best wishes from some of his other clubs he was involved with.
A message from Sheffield Wednesday read: "All at Sheffield Wednesday would like to wish former player and manager Trevor Francis a speedy recovery."
Francis guided the Owls to the FA Cup and League Cup finals in 1993 after taking over as player-manager at Hillsborough two years earlier.