Both players trained at Murray Park on Monday morning, with Rangers saying left-sided Moritz, who has an Italian passport, would not need a work permit and would come as a free agent.
The 26-year-old has spent five years in Turkish football with Kasimpasa, Kayserispor and Mersin Idmanyurd. Faure, 21, was released by Lyon at the end of last season and had a trial spell at Leeds last month. He has returned to Murray Park after training with Rangers last week.
McCoist is looking to add to the five players he has signed since the Rangers newco were handed the Ibrox club's Scottish Football Association membership, before a 12-month transfer embargo kicks in on September 1.
One of the conditions of the membership was that the new company paid off the original club's football debts of about £3million, a third of which was owed to Scottish rivals.
Hearts were owed £800,000 when Rangers were consigned to liquidation, while Celtic, Dundee United and Inverness were among the other creditors. Hearts were due £500,000 this summer and the rest of the transfer money for Lee Wallace in a year's time.
The club has said that they would pay Hearts the final payment when it is due in July next year. Chief executive Charles Green said in a statement: "As of now, Rangers do not owe other Scottish clubs a penny. These debts were incurred prior to the club going into administration and there was no obligation on the consortium buying the club to pick them up.
"From the outset, I have made it clear that I firmly believe the correct thing for the club to do is settle these football debts as a priority and we kept our word. That is what we have done and substantial funds were lodged with the SFA 10 days ago to be discharged to settle the outstanding debts.
"Furthermore, the club was given a written commitment from the SPL in May that it would settle an outstanding debt to Dundee Utd.
"It was frustrating to be informed by the SFA several days after they received the funds that they did not wish to be a 'clearing house' and in fact wanted us to settle the debts directly. Arrangements were then put in place by the club."