They mean both the same thing. What you need to do is to put it in a sentence for context. "I would like to chat with people of the highest level possible"- here the sentence means the people have to be of high quality - i.e President of Russia, bankers, lawyers, President of the USA. If you are talking about learning English then you would say " I would like to speak to people with a high level of English." That sentence is completely different to " I would like to chat to people of the highest level possible." That is a little insulting. :)

Highest possible level

"Highest level possible" is correct.