MEG is capable of recording some of the activity of these deeper regions, but buried in the signal coming from cortical areas and ambient noise. It is possible to reveal some of it by averaging hundreds or thousands of repetitions of the same stimulus - but studying connectivity is a different topic.
Minimum norm source imaging could theoretically help separating the signals coming from deeper vs. superficial sources. But in practice, I'm personally not confident that this is enough for studying functional connectivity from resting state recordings.
@ecoffey and @Sylvain have experience in recording deeper brain structures with MEG (e.g. https://www.nature.com/articles/ncomms11070). They are currently exploring various options for studying connectivity between cortical and subcortical regions.
They could give you more constructive and encouraging feedback than mine on your experimental protocol 