In a statement on the diocese of Arundel and Brighton website, where Cardinal Murphy-O'Connor used to be bishop, Cardinal Nichols who is the current Archbishop of Westminster said: "These loving prayers are a source of great strength and comfort as he calmly ponders on all that lies ahead, all in God's good time.
"May the Lord strengthen him in faith and trust and may the prayers of the Church, which he loves so much, comfort and uphold him."
The Bishop of Arundel and Brighton, Bishop Richard Moth said "As we all know, Cardinal Cormac holds this Diocese in great affection and will, I know, value the prayers of us all at this time", according to Independent Catholic News.
The Church said the 84 year old's health had taken a "defining turn".
Cardinal Cormac, served as Bishop of Arundel and Brighton from 1977, when he was appointed by Pope Paul VI, until 2000 when he was appointed Archbishop of Westminster by Pope John Paul II.
He submitted his resignation as archbishop on reaching his 75th birthday in 2007; it was accepted on 3 April 2009 when Pope Benedict appointed Vincent Nichols as the new archbishop.
In the book The Great Reformer, by the Catholic commentator Austen Ivereigh, it's claimed the former head of Catholics in England and Wales, led a secret campaign for Pope Francis in the Papal conclave of 2013.
He was born on 24 August 1932 in Reading, Berkshire, as one of six children. Three of his five brothers became priests and another played rugby for Ireland.