I lived in a ranch house for 26 years that had the laundry facilities in the furnace room. However, we had all electric in this house and did not have gas, which made it a lot safer. The electric water heater and furnace were on the left wall of the room and the washer and dryer were on the right wall. This was not a big room--about the size of a bathroom. We had no problems whatsoever.

I now live in a much bigger house and the furnace, water heater, washer and dryer are in the basement. They are not close to each other. I do not know how safe it would be to have them together. I would have to ask an expert.

You need to be sure there is sufficient air exchange.

Gas exhaust needs to be vented to the outside and fresh air must replace it. An older house may be able to exchange the air but a new airtight house would need an exchanger.

A clothes dryer dumps inside air to the outside via the fan.

If they have worked before with no issues then it SHOULD be OK.

You don't want carbon monoxide from the burnt gas in the house at all. Install a carbon monoxide detector (the kind that shows the parts per million or PPM) in the vacinity.

Give them room from each other so you can work on them when they break down.