That kept him out of the end of the Blues' season, as well as Wales' summer tour to Australia, but the 25-year-old appears to be on the road to recovery.
But while Davies confirmed that Roberts would miss the start of the Blues' RaboDirect PRO12 campaign, which kicks off at home to Connacht, he is confident the centre will be back sooner rather than later.
"I have been really impressed with Jamie," Davies told Walesonline.
"He's been back in since day one and is working especially hard. Jamie has been outstanding and will, hopefully, be back playing sooner or later.
"We don't know when it's going to be for certain, whether it will be September or October.
"But Jamie has been setting an excellent standard and he will be ready to play for the Blues before the autumn international campaign."
While Roberts will certainly miss the opening encounter against Eric Elwood's men, Davies is more optimistic of having his remaining internationals available to him.
Blues quartet Sam Warburton, Bradley Davies, Leigh Halfpenny and Alex Cuthbert started every test on the tour to Australia but the Blues boss is confident they will be ready for the start of the new campaign.
He added: "We are hoping our internationals will be involved in the first few games of the season. We are working out our plans with the Welsh Rugby Union."
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