The county revealed that the 61-year-old was undergoing hospital treatment for a suspected heart attack and provided a further update on Friday morning.
A brief statement read: "Durham Head Coach Geoff Cook suffered a heart attack yesterday. Geoff remains in hospital and his condition is critical but stable. The club has been inundated with well wishes for Geoff through social media and our thoughts continue to be with Geoff, Judith and his family."
Messages of support for Cook were rife on Twitter, with Durham skipper Paul Collingwood and former England captain Michael Vaughan among those offering support.
Collingwood posted: "All our thoughts with Geoff Cook and his family. Sad sad day."
Vaughan added: "Thoughts and prayers are with Geoff Cook and his family...A great man.. Get well soon Geoff..."
Graeme Swann, taking time out from England's Champions Trophy final preparations, also took to Twitter to wish Cook well, writing: "Just heard the news about Geoff Cook. Fingers crossed for a speedy recovery for him."
England wicketkeeper Matt Prior added: "Thoughts are with Geoff Cook and his family at this time. Fingers crossed for a full and speedy recovery."
Cook played in seven Tests and six one-day internationals for England in 1982 and 1983 and became director of cricket at Durham when they became a first-class county in 1991.
He was named as head coach in 2007, immediately winning the Friends Provident Trophy, and brought the club back-to-back county championship titles in 2007 and 2008. They had never won the championship before.
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