The centre-back was ruled out for three months after suffering the injury in a 1-1 draw with Partick on September 28.
But he could feature for the under-20s next week and could be back for the busy Scottish Premiership schedule at the turn of the year when Saints face Hibernian, Celtic, Dundee United, Motherwell and Ross County within 15 days.
Manager Tommy Wright, whose team host Aberdeen on Saturday, told Press Association Sport: "Steven Anderson has been getting involved in a bit more this week and possibly could train full contact next week, which is maybe two or three weeks earlier than we thought.
"Ideally we would like to get him part of a 20s game next week. There are only two 20s games (before Christimas) so if we could get him two games that will help his progress.
"There is every chance now that he will be involved for the festive period and we had really ruled him out until the first week in January."