Humphrey tweeted: "Our friend & colleague Glenn Hoddle was taken seriously ill at the BT Sport studio this morning".
He added on social media: "Every one of us is right with you, Glenn, sending love and strength".
A spokesman for the Tottenham legend said: "The condition is serious but Glenn is now receiving specialist treatment and responding well".
Is Glenn one of your all time footballing heroes?
"He was a schoolboy at Tottenham when I was there and he was the star player we all looked up to and could never get near".
'Thoughts are with him and his family.
"For that reason there will be no BT Sport Score - but we will be live as usual for the 5.30pm ko at Leicester". You never lose it, Glenn.' Savage also posted a video on his Instagram account of Hoddle smiling during the game, but it was removed after he collapsed at the studios in Stratford, East London.
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Brighton boss Chris Hughton, a long-time team-mate of Hoddle's at Spurs, said: "It's very sad news". Our thoughts are with you'.
After retiring as a player, he was appointed England manager in 1996 and took them to the World Cup finals in France in 1998.
He lost his job the following year after controversial remarks he made suggesting disabled people were paying the price for sins in past lives in an interview with The Times - the remarks all the stranger as he was an ardent fundraiser for disabled peoples charities.
"His family are with him and would like to thank everyone for their support".
Hoddle married second wife Vanessa Colbourn since 2000.
He has three children Zara, Jamie and Zoe from his first marriage.