The 69-year-old was taken to hospital and is reportedly receiving specialist care at the Galenia Hospital in Mexico.
The musician was on holiday in the country with his wife Eileen.
A message shared on Facebook page ‘Bay City Rollers Pen Pal Reunion’ urged fans to pray for Alan.
The message reads: “Posted with permission of Alan and Eileen Longmuir.
“Unfortunately we need to inform all our friends that Alan has been taken seriously Ill whilst holidaying in Mexico.
“He has been admitted to hospital and is currently receiving Specialist Care for a virus that is attacking his vital organs.
He is extremely unwell at the moment but has improved slightly since treatment has commenced. Eileen is with him and has been beside him throughout this awful situation.
It continues: “We know you will all want to send loving, caring and healing thoughts to Alan as we understand how much you care for him. Please keep both Alan and Eileen in your hearts and prayers over the next few days.”
Well-wishers have shared kind messages in support of Longmuir on social media platforms.