Hartson has had two brain operations and is now being reported as no longer critically ill.
His condition does remain serious and Dr Pushpinder Mangat, critical care consultant at the hospital, said in a press statement: "John Hartson is improving gradually and, if this improvement is sustained, we will consider chemotherapy at some point next week.
"He remains seriously, but not critically, ill and under the care of the critical care team at Morriston Hospital."