If I understand you correctly, you are thinking of installing the direct vent system so that the vent that exhausts the fumes will go to the outside, and the vent that feeds the combustion will take air from the indoors instead of outside. If you did that you would be defeating the purpose of a direct vent system -- that it is supposed to be a sealed system that does not affect indoor air in any way. You run the risk of depleting the indoor space of oxygen, which is one of the hazards of ventless systems and the reason they are usually outlawed in sleeping rooms by the codes in most municipalities.

In sum, I do not think this is a good idea. But I have a possible alternative suggestion. If your fireplace is on an outside wall, it might be possible to vent through the wall to the outside instead of up the chimney. Some direct vent systems are designed so that is an available option.

Good luck.