Hartson scored 89 goals during his five seasons with Celtic
Doctors treating former Wales, Arsenal and Celtic striker John Hartson for cancer say he is improving gradually and no longer critically ill.
The retired footballer, 34, has been in a critical condition since undergoing emergency surgery in Swansea.
Hartson was diagnosed with testicular cancer which had spread to his brain and his lungs.
Chemotherapy may start next week. Meanwhile, the star has also received backing from troops in Afghanistan.
The family of the father-of-three, who retired from football 18 months ago, said they are pleased he has been able to make some progress and "is ready to face the next steps in his treatment head-on"
In a statement issued through the NHS trust which is caring for the star, they said:"Our support is stronger than ever.
"Messages continue to flood in and provide us all with a boost, particularly from troops in Afghanistan and the US Marines."
"We thank everyone for thinking of John."
He has had two operations on his brain, the second at the weekend, since the cancer was confirmed earlier in the month.
The first was emergency surgery to relieve pressure on his brain, and the second was a pre-planned neurosurgical drainage procedure.
Critical care consultant Dr Pushpinger Mangat, from Abertawe Bro Morgannwg (ABM) University NHS Trust, said in the latest condition statement that the former player is "improving gradually, and if this improvement is sustained, we will consider chemotherapy at some point next week".
Dr Mangat added: "He remains seriously, but not critically, ill and under the care of the critical care team at Morriston Hospital,"
Swansea-born Hartson was capped 51 times for his country during his footballing career, scoring 14 goals.
He joined Arsenal as a teenager from Luton in January 1995 and, in two seasons at Highbury, made 62 appearances, scoring 16 goals.
The player left Arsenal for West Ham United in February 1997 and continued his career with the Hammers, Wimbledon, Coventry City, Celtic, West Bromwich Albion and Norwich City.
Among the many messagse for him in his fight against cancer was one on Twitter from multi-Tour de France champion Lance Armstrong, who survived the disease himself.