A lid where a magnet attaches is made out of iron.
Iron is a good conductor.
You're trying to build an antenna in a place which is especially well-shielded against radiation. That will be very very difficult.
Omnidirectional from under a manhole cover means "in the earth". If that isn't dry, then there will be little signal there.
Yes, radio waves can penetrate wet soil – as an estimate, with a very sensitive receiver and a very powerful transmitter, you could do up to 10m ground penetrating radar.
But this will not be possible for any receiver that is supposed to receive an AM signal and is remotely related to ham technology (making it on-topic here). For that kind of sensitivity, you'd need extremely low noise figure, and that will be extremely expensive.
All in all, I don't know what kind of radio broadcast receiver for mole people or explosive trigger device you want to build, but I trust physics enough to believe this won't work at your level of insight.
The fact that you're asking about commercial MW inside populated areas (i.e. where there are manhole covers) might indicate you're Britain-based. Now, that'll also mean the broadcasters won't be pushing incredibly much power, making this a bit harder.
To make things more complicated, omnidirectional won't work easily. The reason is simple – the MW/LW wavelengths are far bigger than a manhole, and thus, you can only use high-Q antennas (ferrite core antennas, for example), and those tend to have a very clear preferred direction. Having arrays of these probably won't work either – they'd interact (being all within $\ll\frac12 \lambda$).
Frankly, think about it: As you know, the typical propagation mode for commercial LF and MF is surface wave – the earth's conductive surface forms kind of a waveguide together with ionospehre – and that means that wokring MW reception is based on the fact that at the point of surface, there's little power transport. You could try to make an antenna pick up the displacement currents – but that's going to be freaky business, especially anywhere there's electrical infrastructure (which happens to be the places with manholes).