Lougheed, 84, was recently re-admitted to hospital, but his condition has not been released.
Don Getty, who succeeded Lougheed as premier, said from his home in Edmonton Tuesday that Lougheed's family and friends describe him as very ill.
"He is fighting to get better although the odds are – with his deteriorating health – that he won't be able to, but we're all praying for him."
Lougheed's family released a statement Tuesday morning, saying they are thankful for the kindness and prayers of Albertans, and they are also grateful people are respecting their privacy.
"We will issue a statement when circumstances warrant," said the short statement.
Lougheed, a Progressive Conservative, was Alberta premier from 1971 to 1985. Getty, a cabinet minister in Lougheed's government, served as Alberta's premier until 1992.
Getty called Lougheed a great Albertan and a great Canadian, a politician who has had a tremendous impact on both his province and the country.