Rush was taken to hospital earlier this month and spent around 48 hours in intensive care after collapsing due to breathing difficulties in his home in Cheshire.
The Sun report that medics tended to Rush for an hour and a half, but within 10 minutes of them leaving, he took another turn and collapsed.
Speaking to BBC Sport, Rush opened up on the ordeal, which he says he thought may have been the end.
"I did think the worst and thought this could be it. I couldn't breathe.
"It was very difficult and I'm fortunate the NHS helped me; there were a couple of times where I thought I may not be here (for much longer). But I'm feeling stronger and much better now.
"It was a terrifying experience. I thought it was the end because I couldn't breathe, and I went into a panic attack. Carol was brilliant. She helped me with my breathing, which gave me more time as we waited for the ambulance to come," he said.
Rush also spoke on the support from his wife Carol and Liverpool FC who supporters him as he recovered.
“Carol stayed by my bedside every night without fail,' he added. “Liverpool Football Club were fantastic and provided the support and love which made everything so much better.
“They are a family club after all, and that's what counts in times like this. LFC went above and beyond.”