Long story short, our team is now out of its team leader and our manager is not quite involved in our day to day operations. We're a small team with two more senior guys (another guy and myself) and one more junior.
I will be applying for the promotion and so is my colleague (I think). For the last week, I can sense a small increase in competition, which is normal. However, my coworker's been acting bossy, even so far as instructing me how much time to allow for task XYZ, not to bother with improvement ABC if it takes more than some threshold of time, etc.
He does this in front of other coworkers and this feels like him trying to establish himself as the de facto team leader.
My question is specifically how to address instances where he is making such bossy remarks. If I let them go without commenting I feel like I am enabling him. If I go see our manager, this would look quite childish and may hurt my chances at the promotion. I do not want to pick a fight with him but I would like him to know his behaviour irritates me and I would like it to stop.
Edit: I feel this question is different from this one as it deals more with bullying whereas my question is more how to defuse specific attempts at "managing me".