Bunning, who suffered the stroke Tuesday night in his Southgate, Kentucky, home, was moved from intensive care to a transitional care unit on Thursday night, per the report.
Bunning "has been provided skilled care that is leading him on the road to recovery," the family said in a statement Friday.
"The Bunning family wants to thank the first responders and medical personnel who have been treating dad," the statement said. "We sincerely appreciate the thoughts and prayers of all who are concerned about our father’s health. However, so we can focus our efforts on dad’s recovery, we ask the press to respect our family’s privacy at this time. We will let everyone know as his health continues to improve."
The 84-year old is one of two Phillies pitchers to toss a perfect game in the organization’s history. He accomplished the feat on Father’s Day in 1964.
Along with the Phillies, Bunning played for the Tigers, Pirates and Dodgers in his 17-year career. The righthander, who was enshrined on the Phillies Wall of Fame in 1984, won 89 games and posted a 2.93 ERA in six seasons in Philadelphia.
After his baseball days, Bunning started a career in politics. He served stints in Congress and the U.S. Senate before retiring in 2010.