AC Nanovoltmeter for Arduino alike?
The signal is in frequency range of 10 to 4000 Hz.
  A precision of 2 to 5 nV would be sufficient.


Uh, good luck with that.

Thermal noise power at room temperature is 

$$N = k_B T B\text, $$

with \$k_B\$ being the Boltzmann constant, \$T\$ absolute temperature, and \$B\$ bandwidth.

To observe your 4 kHz signal, you'll need a 4 kHz bandwidth (=9 dBHz) (you'll actually need more – but let's not get into Nyquist and practicality here). 

That leaves us with -203 dBW/Hz + 6 dBHz = -197 dBW. Over a 200 Ω measurement load (can't go lower, or else your measurement will be skewed by the load), due to \$P= U^2 \cdot R\$, that leaves us with 

$$U= \sqrt{RP} = \sqrt{200\cdot 10^{-19.7}}\text{ V}\approx 0.2\text{ nV}\text,$$

and that's assuming the least possible measurement impedance, perfect filterig to reduce the bandwidth to 8 kHz, AND an amplifier noise that has a 0 dB noise figure (which doesn't exist). Notice that this is the thermal noise voltage standard deviation – you'll need to compare that with your required measurement accuracy yourself, you haven't told us.

Realistically, your noise standard deviation would be somewhere in the range of 20 to 1000 nV, even if you built this expertly. But then, external noise sources come very much into play – there's positively very hard work to be done to shield this circuit from all EMI, especially if you want to connect it to a microcontroller (hint: don't, keep your high-frequency switching as far as possible from this).

All in all, this is a project you won't be able to succeed with.