Glenn, 61, who is the former manager of the England team, and also of Tottenham football club, had been working as a pundit on BT Sport when he was taken ill.
The former England manager had appeared on BT Sport's Saturday morning show and had been due to be part of the afternoon live scores show but that was subsequently cancelled.
Gary Lineker passed on his best wishes to Hoddle and his family after hearing the news.
"Hugely worrying news that Glenn Hoddle collapsed at the BT studios earlier".
'Glenn received medical attention on site and he was then taken to hospital.
'Thoughts are with him and his family. "They have also asked to respect their privacy at this time".
Earlier today a BT Sport spokesman told MailOnline: 'Earlier today Glenn Hoddle was taken ill at the BT Sport studio.
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".
Hoddle, who achieved 53 caps for England, was one of the best players of his generation. "We're right with you, Glenn".
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"Everybody across the game is right behind one of English football's greats and we are willing him to pull through".
Hoddle was sacked as England manager after one tournament - the 1998 World Cup - following a newspaper interview in which he implied disabled people were paying for sins from previous lives.
BT Sport presenter Jake Humphrey revealed the news on Twitter.
The couple got together in 1997 after he walked out on his first wife, Anne, the mother of his three children - Zoe, 35, Zara, 32, and Jamie, 26.
Former England and Tottenham goalkeeper Ray Clemence urged Hoddle to "stay strong" and Chris Waddle, another of Hoddle's former worldwide team-mates, said: 'Get well soon, Glenn.
Glenn Hoddle, ex Tottenham Hotspur and England manager, is seriously ill in hospital (file photo).
Hoddle married second wife Vanessa Colbourn since 2000.