I [topic-は] a-bit newspaper [to-に] eye [object-を] pass-through want.
目を通す is a fixed idiom literally meaning 'to pass one's eyes through' — the standard way to say 'to skim, to glance over.' The ~たい ending on 通す creates the desire form 通したい ('want to skim'). ちょっと softens the request and suggests brevity.