The 24-year-old sustained the injury in training this month and was forced to miss the matches against Derby and Hull.
An operation now would mean Fontaine could resume playing around February. Another option could see the Londoner rest for around a month and then attempt a comeback.
"We have to decide whether to leave it to rest and recuperation for the next four weeks or so, or whether to go for surgery straight away," said City boss Keith Millen. "It is a difficult call to make and that is why we are seeking a second opinion. We want as much information as possible before we make a decision.
"We could leave it to rest, but there is no guarantee that will work. If after a month Liam still needs surgery, then we are looking at him being out for most of the rest of the season.
"He has been one of our most consistent performers this season and we want to take the option that makes him available soonest."
Source: PA
Source: PA