The Glasgow giants could wrap up the Scottish Premier League if they win and other results go their way but Ledley knows just how dangerous the ninth-placed Hibs can be with 20-goal Wolves loanee Leigh Griffiths in tow.
"Hibs have done really well and have some good individual players," the Welshman told this week's Celtic View.
"Leigh Griffiths has done well for them. They are organised, but hopefully we can break them down and beat them for the first time this season. We know it will be difficult because of the way they play but with our home form, we can achieve it.
"They have got dangerous players going forward so we will need to try and keep at things on the back and try and keep a clean sheet.
"We always feel we will always score goals at home and that's what we will need to do in the next game but keep the back door shut."