"The neurological evolution of the patient Severiano Ballesteros remains favorable. He continues to receive rehabilitative treatment and will probably leave the intensive care unit next week," Madrid's La Paz Hospital said in a statement.
In a statement issued earlier this month, the hospital said the 51-year-old had regained consciousness and was able to able to talk to his famiy members.
Ballesteros, who collected 87 titles before knee and back problems forced him to retire last year, was taken to the hospital on October 6 after he collapsed and briefly lost consciousness at Madrid airport.
He announced he had a brain tumour on October 12 after first personally informing his ex-wife and their three teenaged children of the diagnosis.
Two days later, he underwent surgery to remove the tumour, and on October 16, he had a second operation to ease a build-up of fluid in the brain.
On October 24, Ballesteros underwent a third successful operation to ease swelling in his brain and remove the remains of a tumour.
Regarded as one of golf's all-time greats, Ballesteros won five majors.
He won the British Open in 1979, 1984 and 1988 and became the first European to win the Augusta Masters in 1980, an achievement he repeated in 1983.
Ballesteros was also an influential figure in the Ryder Cup, winning 20 points from 37 matches and captaining Europe to victory at Valderrama in 1997.