BT Sport presenter Jake Humphrey revealed the news about the former Tottenham and England player, who now works as a TV pundit and turned 61 on Saturday.
Humphrey tweeted: "Our friend & colleague Glenn Hoddlewas 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."
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.
He managed England between 1996 and 1999, taking the team to the 1998 World Cup.
Former England team-mate Gary Lineker wished Hoddlewell, writing on Twitter: "Hugely worrying news that GlennHoddle 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.
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.
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