The 36-year-old retired from the game in 2016 and had been working on getting his UEFA training licence.
The midfielder starred under O'Neill in his final season with the Scottish giants, scoring in a Champions League match against Lyon that helped seal his big move away.
"I gave him his debut at Celtic", O'Neill said at today's press conference.
"The news, we heard about it just recently, we didn't know how bad it was".
"All thoughts go out to him and his family".
For Ireland, Miller earned 21 senior caps under Brian Kerr, Steve Staunton and Giovanni Trappatoni. We are thinking of him and we hope he can pull through and he's strong anyway.
Miller joined Leeds United on loan from Manchester United and also had spells with Sunderland, QPR and Hibernian.
Later in his career, Miller would spend some years in Australia's A-League, before returning home to play with Cork City in 2015 before heading overseas again, joining the Wilmington Hammerheads in North Carolina. He scored once, in a friendly win against Sweden in 2006, and what a goal it was.
Many former teammates have sent their good wishes to the midfielder. All thoughts go out to him and his family.
John Hartson, who played alongside Miller at Celtic, tweeted: "My thoughts are with Liam Miller and his family this morning".
This story originally appeared in the Evening Echo.