How can I address my career future with my current PI? I'm currently midway through my first Postdoc gig, I got a 1 year contract and haven't heard a word from my PI concerning any possible extensions. I only have 6 more months left in my program, and I was wondering whether I should:


Ask him directly whether he is considering to extend my contract.
Start looking for other jobs without consulting with him first.


I know I'm under a grant that runs out shortly after December (my contract is due on February), and we might or might not have an extension for that. The answer should come around September's end, but I'm afraid it'll be too late to look for another postdoc then, I'm under a J1 visa in the USA, and I'm worried that the immigration process to extend it and the whole hiring process might take considerable longer than 5 months. 

AS professors and more experienced professionals, what would you recommend to do, I'm also wondering whether asking him if I should look for another job might strain our relationship.
Your advisor has the duty to inform you if you are meeting expectations, and to notify you in a timely manner if your contract will be renewed or not. Politely bringing this up at the end of the meeting should not cause conflict with your advisor—unless your advisor is a control freak (in which case it's not exactly a bad thing that you'll need to move on!). 

However, I would have this conversation as soon as possible, as the end of your contract will be here quite soon. You should inform him, if you'd like to continue working with him, that such is the case. You should also politely mention that if the finances aren't secure for a commitment, that you will need to consider additional job opportunities to ensure that you are not "stuck" looking for a job without a current source of income.