BT Sport presenter Jake Humphrey revealed the news about the former Tottenham and England global player, 61, who now works as a TV pundit.
Former footballer Chris Sutton said: "Thoughts and prayers for Glenn Hoddle and his family after he was taken ill today".
According to Hoddle's official Twitter feed, he was scheduled to analyse the 3pm kick-off between Brighton & Hove Albion and Wolves for BT Sport as part of their live Score show. The nature of the illness is not yet clear.
Soon after the news became public, the stream of support, flowing from so many corners of the football landscape, testified to the popularity of a man who both played for and managed England.
Former England great Gary Lineker - who along with Hoddle was a pivotal player in England's 1986 World Cup finals campaign where they reached the quarter-finals - chipped in with his own message. "Our thoughts are also with his family and friends at what will be an extremely hard time for everyone who knows him". Thoughts are with him and his family.
A spokesman for Hoddle earlier confirmed the football legend was taken ill.
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The Football Association, via the England team account, wrote: 'Worrying news.
Is Glenn one of your all time footballing heroes?
Hoddle, who was celebrating his 61st birthday, is "responding well" to specialist treatment after the incident on Saturday morning. "Everyone of us is right with you Glenn, sending love & strength". West Ham EPL clash later on Saturday. Our thoughts are with you'.
Tottenham tweeted: "Everybody at the Club sends their best wishes to @GlennHoddle for a full and speedy recovery after he was taken ill this morning".
'Glenn is now in the care of the professional NHS medical services, who have also been exemplary in helping him and the family during the last 24 hours.
Hoddle capped 53 times for England and was a star midfielder for Tottenham, widely considered to be one of the best players of his generation. He spent 12 years with the London club before joining Monaco.