The 22-year-old joined Rochdale on loan until January last month and was playing for the League One club in their Checkatrade Trophy match against Bury on Tuesday when he sustained the injury.
“He’s got a fractured cheekbone” said Rochdale manager Keith Hill.
“It was a clumsy accident that led to Connor having to come off, and unfortunately for Connor, he’s going to be out for 12 weeks. That’s a big miss for us and it’s a shame for him.
“He’s back at Liverpool [for treatment] because he needs an operation but we’re in contact. We wish him well in his recovery.