The former England manager was taken seriously ill at the BT Sport studios on his 61st birthday, with BT’s afternoon live scores show cancelled as a result.
A spokesman for Hoddle said: “Earlier today Glenn collapsed at the BT Sport studios. He received immediate medical attention on set and was subsequently transferred by paramedics to hospital in London.
“The condition is serious but Glenn is currently receiving specialist treatment and responding well.
“Glenn’s family are with him and would like to thank everyone that has sent their support. They have also asked for their privacy to be respected at this time.”
In statements released to the Press Association, England manager Gareth Southgate and Football Association chairman Greg Clarke both sent their support.
Southgate, who played under Hoddle for England, said: “My thoughts and prayers are with Glenn Hoddle and those closest to him following today’s distressing news. Everybody across the game is right behind one of English football’s greats and we are willing him to pull through.”
Clarke added: “All of us at Wembley and St George’s Park are thinking of Glenn and hoping for positive news. Our thoughts are also with his family and friends at what will be an extremely difficult time for everyone who knows him.”
BT Sport presenter Jake Humphrey revealed the news about the former Tottenham and England player, who now works as a TV pundit.
Humphrey tweeted: “Our friend & colleague Glenn Hoddle was taken seriously ill at the BT Sport studio this morning. For that reason there will be no @btsportscore - but we will be live as usual for the 5.30 ko at Leicester. Everyone of us is right with you Glenn, sending love & strength.”
BT did show the evening Premier League match between Leicester and West Ham and, speaking at the start of the coverage, Humphrey said: “Whatever Glenn Hoddle is for you, whether he is one of the best footballers the country has ever produced, a wonderful colleague or a much-loved family member, the outpouring of love and support today has been quite something to behold.
“We at BT Sport add to that and we are standing alongside you Glenn and sending you the very best for a speedy recovery.”
Hoddle is regarded as one of the most talented players to represent England in recent decades. As well as Tottenham, he also played for Monaco and Chelsea and managed, among others, Chelsea, Southampton and Spurs.
Messages of concern and support quickly began to pour in.
Former England team-mate Gary Lineker wished Hoddle well, writing on Twitter: “Hugely worrying news that Glenn Hoddle collapsed at the BT studios earlier. Thoughts are with him and his family. Come on Glenn.”
The Football Association, via the England team account, wrote: “Worrying news. Get well soon, Glenn Hoddle, we’re all behind you.”
Tottenham and Chelsea also sent their best wishes to their former player and manager, as did England captain Harry Kane who said his thoughts were with Hoddle.
Southampton manager Mark Hughes, a former team-mate of Hoddle at Chelsea, said after his side’s 0-0 draw with Newcastle: “I’ve only just heard. He’s in good hands by all accounts and we hope he’s able to come through this situation.
“I’m not sure how serious it is but clearly when these things happen there is a little bit of concern to the welfare of someone I know well, someone who signed me for Chelsea and was manager here when I was a player.
“We and everybody in football wishes him well because he’s a fantastic football guy.”
Brighton boss Chris Hughton added: “It’s very sad news. Glenn’s somebody I’ve known from the age of 12, 13. He was a schoolboy at Tottenham when was I was there and he was the star player that we all looked up to and could never get near.
“I, of course, worked under him when he was (Tottenham) manager as one of his coaches.
“So certainly my thoughts are with him and my prayers are with him. He’s got a strong character, Glenn, and I’m sure he’ll battle through it.”
Hoddle won 53 caps for England while as manager he took his country to the 1998 World Cup finals in France, qualifying on the back of a memorable 0-0 draw away to Italy.
He lost the job the following year after expressing controversial views on reincarnation in a Sunday Times interview.
Former England goalkeeper Ray Clemence, who was a goalkeeping coach during Hoddle’s England reign, urged him to “stay strong”.
Michael Owen, who scored a memorable World Cup goal for England under Hoddle against Argentina in 1998, said: “Just hoping Glenn Hoddle is ok after falling ill today. Great manager and a great man.”
A two-time FA Cup winner with Spurs, Hoddle also had success on the continent, lifting the UEFA Cup with Tottenham in 1984 and the Ligue 1 title in Monaco in 1988.