You'd have to know the input impedance of your meter to figure how much leakage current there is.
0.001mA (1 microampere) of leakage in a 1MΩ input impedance meter is 1mV measured on the meter; with a 10MΩ meter, it's 10mV.
And depending on your meter, the input impedance may get bigger as you set the meter to measure lower voltages.
But you almost have to unsolder the cap because the meter's resistance is in parallel with the grid reference resistor of the next stage. Because leakage is leakage current and a measurable voltage is a byproduct, the meter's parallel resistance makes the measured leakage look smaller.
If you know you had a very high impedance meter (I've got one that will manage 200MΩ input impedance on these low ranges) you could measure without removing the cap. Or if you had a a very low-current meter (again, I've got one good down to 1pA) you could lift the leg of the cap and place the meter in series with the circuit to measure the leakage directly. That won't work with meters that only get down in the 10-100mA range.
So what to do? Your meter is probably a 10MΩ impedance (check specs to know for sure). If the bias voltage is very large (like 10's of volts in output tubes) or the effective grid resistance is small (like 100-220k in output tubes), relatively high leakage is still workable. If the leakage causes a 0.1v shift in a preamp stage (where bias might be as little as 1v), that could be significant.
But you're probably using film caps of some kind, and you'd like to see the extremely low leakage these should be exhibiting. Assume a preamp stage, 1v of bias and a 1MΩ grid resistor. 0.05v is maybe as much bias-shift you'd want to tolerate due to leakage, which represents 0.05uA of current. The same current across 10MΩ would measure as 500mV. You might call that too much and replace the cap.
It's really your call; severity of leakage depends on if and how it impacts the circuit. Some guys used to repairing and calibrating test gear tolerate no measurable leakage. But make sure to measure again with the new cap, to make sure you're not detecting some other issue.