Based on the paper linked to the word ‘bloodstream’ in this article, the authors stated that:

“Intramuscular injection is the method of installing medications into the depth of the bulk of specifically selected muscles. The basis of this process is that the bulky muscles have good vascularity, and therefore the injected drug quickly reaches the systemic circulation and thereafter into the specific region of action, bypassing the first-pass metabolism.”

Assuming that LNP can enter the bloodstream (or systemic circulation) in the same manner as drugs, it means that LNPs can pass through the blood vessels of muscle tissues. But please note that this is just an assumption based on how drugs work in an intramuscular injection.