Hoddle collapsed at BT Sport studios, on the day the former Tottenham midfielder - who was capped 53 times by England as a player - turned 61.
He was taken ill at the studios of BT Sport, who consequently cancelled their usual Saturday scores and results show.
BT Sport presenter Jake Humphrey tweeted that Hoddle "was taken seriously ill".
Later on Saturday, a spokesman for the 61-year-old said that Hoddle's condition was "serious" but the former England manager was "responding well" to treatment.
"His family are with him and would like to thank everyone for their support".
"Earlier today Glenn Hoddle collapsed at the BT Sport studios. All our thoughts are with Glenn Hoddle and his family", he said on Twitter.
After quitting active football he managed Chelsea, Southampton and Tottenham in the English top flight, as well as Wolves then in the second division as well as helping Swindon Town gain promotion to the Premier League in 1993. Obviously we all wish him and his family well and I hope he can make a speedy and full recovery.
Glenn has three children, Zara, Jamie and Zoe from his first marriage to Christine Stirling, who he was with from 1979 to 1998. "He's got a strong character, Glenn, and I'm sure he'll battle through it".
Argentinian great Ossie Ardiles - who played alongside Hoddle in the 1981 FA Cup replay triumph over Manchester City - said his thoughts were with his former team-mate.
BT Sport presenter Mark Pougatch said: "You will understand why there's no BT Sport Score this afternoon".
"Thoughts are with his family". You won't meet a nicer guy than Glenn.
In statements released to the Press Association, England manager Gareth Southgate and Football Association chairman Greg Clarke both sent their support.