Hoddle, who spent the bulk of his playing career with Tottenham Hotspur and played for Chelsea, French club AS Monaco and Swindon Town, was working for BT Sport as a pundit on his 61st birthday on Saturday when he collapsed.
"Glenn remains in a serious condition in hospital after suffering a heart attack yesterday. He continues to respond well to treatment," the spokesman said.
"Doctors have advised the most important thing for Glenn is time to rest. Therefore, his family have reiterated the request for their privacy to be respected during this period."
Hoddle was one of English football's top players during the 1980s, winning 53 England caps before managing his country from 1996 to 1999.
He spent 12 years at Tottenham, playing 490 games in all competitions and winning the FA Cup and the UEFA Cup.
Hoddle guided England to the 1998 World Cup finals in France but his tenure ended acrimoniously when his contract was terminated after an interview in which he expressed controversial beliefs about disabled people.
He went on to manage Southampton, Tottenham and Wolverhampton Wanderers before working as a football television pundit.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
