The dryer vent hose to the outside, has a small gap between the hose and the cement block. What is a good product to use. Caulking or some other fireproof
Product? Gap is about 1/2 inche

Any good caulk will work. Doesn't the hose have an air deflector that seals against the house?

Yes the outside has louvers that open when the dryer is operating and close
Then the dryer is off. It is attach to a flat plate that is flush to the house wall.
Only on the inside do you see a gap. It may not go to the outside. But the gap should be closed

Put backer rod in the space and then caulk.

You cannot seal such a big gap with caulk, but for sealing I use GE Clear Silicone caulk. It's heat-proof to 800°. Foil tape is the best, but you need a piece of sheet metal for the gap, but you cannot use screws, so clean very well and use foil tape. In a year you will have to remove it all to clean the dryer and vent, so don't make it so it will not be easy to take apart.

Okay