Apparently so, but LG has evidently denied the speculation now. According to the rumor, Google is ready to obtain a 35% stake in LG to the tune of 2.5 trillion won ($ 2.2 billion), which would have made it the largest shareholder, though the block purchase wouldn't guarantee it management participation, too.
What synergies could Google have from being an LG stakeholder, is anyone's guess, despite that LG has made Nexus gear before. Google, after all, tried its phone-making luck with Motorola, but quickly divested of its purchase. LG is, of course, not Motorola, and it is making TVs as well as phones and tablets, but still the whole rumor can raise an analyst's eyebrow or two.