"The Anderson family -- wife, Carol; sons Lee and Albert; and daughter Shirley Englebrecht -- wishes to express appreciation to all friends and fans for the support and kindness they have shown throughout Sparky's career and retirement," the statement read.
"The family is particularly grateful for the respect for privacy the national and local media has demonstrated during this trying period."
Anderson, 76, led the Reds to World Series titles in 1975 and '76 and guided the Tigers to a World Series victory in 1984 to become the first manager to win the World Series with both a National and American League team.
He managed the Reds from 1970-78, leading the club to the World Series four times and finishing with a 863-586 record. He was the skipper of the Tigers from 1979-95 and posted a 1,331-1248 record while winning AL Manager of the Year honors in 1985 and '87.
"We are very sad to hear the news of Sparky's failing health," Reds president and chief executive officer Bob Castellini said in a statement. "Every day here we are reminded of his contribution to the success of this proud franchise. The Reds' family offers its prayers and support to Sparky and his family during this difficult time."
Anderson compiled 2,194 wins over his 26 years as a manager to rank sixth on the all-time list. He's also the winningest manager in the history of the Tigers with 1,331 victories.
"The Tigers organization is saddened by the news of Sparky's illness. We will keep Sparky, his wife, Carol, and the entire Anderson family in our thoughts and prayers," the Tigers said in a statement.
"Sparky led one of the most beloved teams in franchise history to the World Series title in 1984 and remains the winningest manager in franchise history. His contributions to the Detroit Tigers remain a significant part of the club's history."
He remained active in the Detroit community after his retirement, continuing his role with CATCH, which he founded in 1987 with the goal to help improve the quality of life for sick, injured and at-risk pediatric patients who receive care from Children's Hospital of Michigan and Henry Ford Hospital.
Anderson attended the reunion of the 1984 Tigers at Comerica Park in September 2009 and the Hall of Fame induction ceremony in Cooperstown, N.Y., earlier this year.
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.