I wouldn't be surprised it it doesn't already exist, but I'd expect it to be 16+ bits versus only 14 bits.
STM32F072VBT6 could do it at 12 bits. Just add hardware to interface the DAC and ADC to the phono jacks. STM32F373 series has a built in 16 bit ACD. It would need an output DAC of 14 or 16 bits. I'm betting some manufacturer already has one with the appropriate 16 bit ADC, 16 bit DACs and audio analog IO hardware to allow direct connection the the phono jacks. Ask over in the "Microcontrollers & FPGAs" area if somebody knows of existing ones.
A quick search turned up hundreds of single board computers that have 16 bit stereo audio input and output interfaces, plus advanced communications so the data could be transmitted over the network, or a dedicated set of wires.
If you want to make 10,000+ of them, custom silicon is a good option because it can handle most of the analog as well as the digital, and put it into a small but simple to solder package. That would simplify the schematic and PCB greatly.