According to The Telegraph, the golfer's family have stopped taking phone calls and have asked the hospital not to give out any information beyond a statement.
"Severiano Ballesteros has left the intensive care unit where he was admitted due to a partial epileptic fit, and is receiving the prescribed treatment. He is in a stable condition," a hospital statement said.
Neurologists had already carried out brain scans. "Everyone is worried that it could be something very bad," said one of Ballesteros' oldest friends.
Ballesteros released his own statement on Thursday in which he thanked everyone who had expressed concern. "I hope you will understand that it is difficult to answer all your messages due to the great number I am receiving," he said. "I want you to know that they make me feel very good."
Colin Montgomerie said he was speaking for all his fellow professionals when he wished Ballesteros a speedy recovery. "What we're hearing puts everything into perspective in a heartbeat," said the Scot, who played to great effect under Ballesteros' captaincy in the 1997 Ryder Cup at Valderrama.
Ballesteros is a winner of five majors and 87 titles.