The 60-year-old Wythenshawe and Sale East MP’s wife Wyn and three grown-up children are at his bedside and have asked for “prayers and privacy”.
In a statement published by the Manchester Evening News, the family said: “Yesterday, December 30, Paul Goggins MP was taken ill while out running with his son near his home.
“He was taken by ambulance to Salford Royal, where he remains seriously ill.
“He is receiving the best care. His family are with him and ask for prayers and privacy.”
The Labour leader Miliband described Mr Goggins as “one of the most decent, kind and assiduous members of Parliament.”
“The news of his serious illness is a huge shock for people across the Labour Party and for his friends throughout Parliament,” he said.
“All of my good wishes and the thoughts of our whole party are with him and his family.”
His remarks were echoed by fellow Labour MPs.
Lucy Powell wrote on Twitter: “All my thoughts are with Paul Goggins and his family. I very much hope for his speedy recovery. He is a really decent, genuine person.”
And Barbara Keeley posted: “Prayers & thoughts with Wyn and the Goggins family – so sorry to hear of Paul’s sudden illness.”