Can I direct the audio signal from Apple TV?

I have the following equipment:

Equipment

I have all my music files stored in iTunes on the pictured iMac. When I play music it follows a path from the iMac through the Time Capsule to the Airport Express. The Airport Express connects by hard wires to a stereo power amplifier (that has no volume controls, selector switch, or additional connections available) and from the amp to the stereo speakers. I control all of this directly from the iMac using the iMac's volume control. This all works great and sounds great.

As the diagram also shows, I have an Apple TV that connects to the TV.

In our house we predominantly watch Netflix or other content via the Apple TV.

I'd like to direct the audio signal from the Apple TV to the Airport Express and thus to the amp and speakers.

I know I could put in an additional device and hardwire the TV's audio outputs, stereo amplifier, Airport Express into it (essentially use it as a switching device), but it just seems that I should already have everything one really needs already.

Any way to do this?

Follow up...

Looking at the suggestions offered and doing a bit more research on my own it seems like the easiest solution would look something like this:

solution

This idea adds an analogue switch, which both the TV's analogue audio output and the Airport Express's analogue audio output (the Airport Express has a built in digital to analogue converter, DAC) run into. The switch's output goes to the amplifier.

This solution depends on a few of things:

The TV's audio output has sufficient level to drive the amplifier.
The TV's volume control (from its remote) can adjust the level of its audio output enough that the speakers reach desirable listening levels -- both low enough and loud enough.
Nothing nasty happens switching between audio sources.

A remote control for the switch would be nice.

Any suggestions for such a device?

Solution 1:

The Apple TV can replace the Aiport Express (for audio duties). I took this route and it works well most of the time as a drop-in replacement for the Aiport Express. I moved the Airport Express to the other end of the house to extend my Wifi network.

But you will need an extra bit of hardware, as your amp doesn't have optical in. You'll need a digital to analog audio converter (here's one on Amazon). They are usually $40-$60 in price.