A Queensland Rugby Union statement on Thursday morning revealed that Lynagh, who won the World Cup with Australia in 1991, was undergoing tests in the Royal Brisbane Hospital to discover the cause of the illness.
The 48-year-old was admitted to hospital on Monday night after complaining of blurred vision and headaches following a long-haul flight from London, where he now lives, to Brisbane.
"Former Queensland Reds and Wallabies captain Michael Lynagh was hospitalised in Brisbane on Monday night after suffering a stroke," the statement read.
"Mr Lynagh remains in a stabilised condition in the Royal Brisbane Hospital and is undergoing tests in an effort to discover the cause of the illness.
"The Lynagh family has requested their privacy be respected at this time.
"The thoughts of the entire Queensland Rugby community are with Michael and the Lynagh family."
Fellow Queensland and Australia World Cup-winning team-mate Tim Horan tweeted this morning that Lynagh was walking around.
"Michael Lynagh undergoing MRI this morning. Up and walking," he wrote.
Former Wallabies captain Andrew Slack, who wrote Lynagh's biography, told ABC Radio: "He lives in the UK now and he is back here to visit his family and just felt unwell on Monday night and headaches and various things and ended up in hospital, which I think was initially diagnosed as a stroke-type of event.
"But the doctors are still trying to work out exactly what has happened.
"Clearly he has got some issues from it some blurred vision and stuff.
"But I am led to believe he got up and went to the toilet at one stage, so there's not a lot known, but he's stayed very fit since retiring some years ago and so I think she is a bolt out of the blue."
Lynagh won 72 Test caps and retired from international rugby in 1995 as the world record points scorer with 911, a total which remains an Australian record.
An inspirational playmaker Lynagh, who also won 100 caps for Queensland, made his Test debut in 1984 and he was part of Australia's Grand Slam-winning team later that year.
Lynagh was vice-captain of Australia's World Cup-winning side in 1991 and he scored the late winning try against Ireland in the quarter-finals.
After captaining Australia to the quarter-finals of the 1995 World Cup, Lynagh retired from international rugby and joined Saracens at the start of the professional era.
Lynagh was the club's first major signing after Nigel Wray had taken control of the club and he helped attract Philippe Sella, Francois Pienaar and Kyran Bracken to the club.
Lynagh spent two years at Saracens, guiding them to a 48-18 victory over Wasps in the 1998 Tetley Bitter Cup final and he has been enrolled in the club's Hall of Fame.
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