Van der Sar, 52, who spent six years at Manchester United before leaving in 2011, was most recently a director at Ajax but quit before the end of last season after the club finished third in the Dutch league and missed out on Champions League football for the first time since 2009.
Ajax provided a further update on Saturday in a statement which read: "Edwin van der Sar will remain in intensive care for the time being.
"His condition is stable but still concerning. Ajax shares this information on behalf of Annemarie van der Sar, Edwin's wife.
"The Van der Sar family, along with Ajax, is grateful and deeply touched by the many messages of support."
His wife Annemarie suffered a cerebral haemorrhage in 2009 when he was a player at Old Trafford but made a full recovery.