Digital potmeter in transimpedance amplifier feedback
Digital pot could have more noise compared to a discrete resistor.

The amplifier can be split into two (2) stages.
1st stage is a fixed gain transimpedance amplifier.  (One could call it a pre-amp.)
2nd stage is a variable gain amplifier with a digital pot.  The 2nd stage shall have a strong input signal from the 1st stage, so the noise from the digital pot would have only a small impact.

There is also a concern that a digital communication signals from which the digital pot receives its setting (e.g. I2C, SPI, etc) can crosstalk into the analog path of the pot.  I've seen that happen with D/A converters.  Check this with an oscilloscope: trigger the scope from the digital lines, observe the analog signal.  If you see this problem, it can be addressed by creating a quiet period without digital communication, during which the measurement would be made.