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 on Saturday read: "Trevor Francis' family have contacted the club to express their sincere thanks for the overwhelming messages of support they have received from Blues fans in the last 24 hours.
"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.
"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 Twitter message from Manchester City read: "We would also like to send our best wishes to former #MCFC player Trevor Francis who was taken ill on Friday. Get well soon, Trev!"
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.
Mark Bright, a member of that Wednesday team, tweeted: "I'm stunned to hear that my former #swfc manager Trevor Francis is in hospital after suffering a heart attack. #getwellSoon."
Former England team-mate Gary Lineker also used Twitter to convey his thoughts.
Lineker said: "Shocked to hear Trevor Francis has suffered a heart attack. Thoughts are with him and his family #getwellTrevor."
Mick Rathbone, a former Birmingham team-mate, said last night: "Just heard bad news about Trevor Francis.... spoke to him at length last sat... best player in england in late seventies #getwellsoon."
Francis remains the youngest player to have featured in a first-team game for Birmingham having made his debut in September 1970 at the age of 16 years and 139 days.
He is regarded as one of the finest players to have represented the club and helped them win promotion back to the old Division One in 1972.
He went on to score the winning goal for Forest in the 1979 European Cup final against Malmo, before helping the team reach the 1980 final against Hamburg - although he missed victory in that game through injury.
He left Forest in 1981, going on to play for Manchester City, Sampdoria, Atalanta and Rangers.
He won 52 England caps and represented his country at the 1982 World Cup, later having player-manager spells with QPR and Wednesday.
He took over as Birmingham boss in 1996 and led them to the 2001 League Cup final, which they lost to Liverpool on penalties.
Since leaving Birmingham he has had a spell as manager of Crystal Palace from 2001 to 2003 and worked extensively as a television pundit.