In plain words
Just as all-pervading space, because of its subtlety, is not tainted, so Ātma, present throughout the body, is not tainted.
Word for word
As all-pervading space, because of subtlety, is not tainted, so the Self, present everywhere in the body, is not tainted.
यथा सर्वगतं सौक्ष्म्यादाकाशं नोपलिप्यतेसर्वत्रावस्थितो देहे तथाऽऽत्मा नोपलिप्यते
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
किमिव न करोति न लिप्यते इति अत्र दृष्टान्तमाह —
यथा सर्वगतं व्यापि अपि सत् सौक्ष्म्यात् सूक्ष्मभावात् आकाशं खं न उपलिप्यते न सम्बध्यते, सर्वत्र अवस्थितः देहे तथा आत्मा न उपलिप्यते ॥ ३२ ॥
In plain words
But how is it that he does not act, and nothing sticks to him? To answer that, an example is given —
Think of space. It reaches everywhere, touching everything, and yet nothing ever sticks to it or holds it down — precisely because it's so fine, so subtle, that nothing can actually get a grip on it. The Self is exactly the same. Even though it seems to fill the whole body, present in every part of it, nothing about the body ever stains it.
Close to the Sanskrit
"How indeed does he not act, is not tainted?" — with regard to this, he states an illustration —
Just as space, the ether, though all-pervading, all-pervasive, existing everywhere, is, because of its subtlety, its subtle nature, neither tainted nor bound — likewise the Self, present everywhere in the body, is not tainted.