It depends. In most circumstances, I think you should at least be discussing this internally.
OP, I get the impression that your colleague would be surprised if their contract was not extended.
If it surprises someone, they either haven't been given sufficient and appropriate feedback, or they were oblivious to feedback. A lack of feedback indicates an issue with the quality of management and supervision that should be addressed internally.
Many juniors - fresh out of college or uni - still need to work on the self-management and communication skills required to function in the workplace. In my opinion, a junior should be entitled to a little leeway.
What should the organization be doing?
A manager or supervisor should have informed your colleague that they are under-performing and outline what improvement they should show before the end of the probation. Personally, I'd schedule a bi-weekly feedback session with an experienced team member (such as my Scrum Master), and I'd instruct junior to make notes of interactions with colleagues, reflect on these and discuss their reflections with their new mentor. I want my team members to take feedback from each other without me using the ban hammer as an incentive. If they learn to receive feedback and to objectively assess their own performance, they will be an excellent team member.
I will have the same initial conversation with someone with more experience, but I will be less inclined to invest in coaching. In my current team, sufficient feedback would have been provided on a daily basis. If you don't catch on, you get to look back on getting fired as an educational experience. Some people need that, I definitely did.
So, what's the right thing for you to do?
That depends entirely on company culture and the risk you are willing to assume. Staying in your lane is definitely the safest option. In the right company culture, you should at least be able to talk to your manager in private. I'd want to ask my manager (1) if my new colleague has been informed and (2) whether or not the manager thinks the team could have done anything to correct the issue at an earlier stage.
If my colleague seems like a nice guy (and it seems like he could still salvage the situation) I'd invite him for a beer or lunch and talk to him about the sentiment in the team. If he's unaware and not getting the feedback he should be getting, that feels like an injustice to me. I would not give him advice, but I would tell him that he can come to me for advice.
This would not result in blowback in my current team and organization. And I don't work in an at-will state. That is a luxury that you might not have.