I've been in my internship in a state-owned enterprise for six months so far, and this is my last month there. Since I started, they assigned me a mentor who would make sure I and the rest of my workmates who are on their internship as well are assigned tasks suitable for our skills.
From the beginning, I was the only one able to do advanced tasks, so I've been separated from the rest of my workmates and instead of working with them, I've been working where the permanent employees are.
I've always felt welcomed and integrated by them. During my internship my mentor wasn't the person who assigned me the tasks, but an employee who is sat next to him. In fact, he's who decided I should work around them instead of being with the rest of the interns. This man has always made everything possible to make me feel comfortable. For example, when one day I was going to be reprimanded for something that wasn't my fault he helped me telling them it wasn't my fault.
When we have nothing to do, we usually chat. And I love it when we do, because we share some interests and he happens to have the same education as me. Not to mention that he's responsible for things I would like to do in my career in the future, so I'm aspiring to become like him. One day I told him I'm good at what we do because rather than going out I prefer staying at home studying and he told me it was OK. I've consulted him about the possibility of obtaining some online certifications sometimes and he always encourages me saying I'll obtain it easily. He also gives me useful advice, and he tells me how life was before, what he liked to do when he was young, etc.
I'll really miss those moments once I finish my internship, and I really, really look forward to becoming friends with him or at least get to know him more. However, my main worry is that there's a big age difference. He's probably in his 50s whereas I'm 30 years younger (I am a male, too). So I have a strong fear of rejection because of this.
In any case, before my departure I'll talk to him in private in order to thank him for everything and tell him it was nice to meet him, and that's when I'm planning to come up with my interest of becoming friends with him or getting to know him better.
However, I honestly don't know how to ask him. How do I do it?
What's my intention
Friend is a very wide concept. When I say I'd like to become friends with him I mean I would like to keep in touch with him afterwards. But I don't just mean the typical New Year greeting or letting him know how I'm doing. I would like to keep doing what we've done so far: chat about our interests, how the industry was when he was young, ask him for advice or support... in person. That is, not limiting the contact to text messages or emails. I don't want to go out drinking or something similar. I can't even do that with people who are my age... But instead I'd like to meet in calm and formal places like a café, for example.
But honestly, my interest is mainly personal than professional. I just want to establish a friendship based on respect with someone whose career is similar to my ideal one, a role model.
Of course, I won't force anyone to do something they don't want to. But I would like to let him know I'm willing to sacrifice some of my free time to spend it with him. How to do it is what I'm struggling with.
Regarding @OldPadawan's comment
@OldPadawan has explained very well the perspective as seen from the other side, but I would like to explain what led me to believe I could get to befriend this employee. As I said, I was the only one of the interns group able to do tasks the rest couldn't. This is something that has happened to me during my life. I'm not and expert or a genius at what I do, it's just that I like researching and reading articles about what I like. I can relate to @OldPadawan because I like helping people, and I've helped many classmates back when I attended school with the subjects they found difficult.
Maybe I'm mixing concepts, maybe it's not the same to assist someone who's in your class or who is your age, but I've always found it frustrating how my help is not truly appreciated. To be honest, I expect nothing in exchange when I help someone, but when I help them and the only feedback I receive when we drift apart is a yearly text message (that's the best thing that has happened so far, the rest have completely forgotten about me) I feel empty. Being an introverted person doesn't help, so that's the best approach I can do to exchange some words with someone. I've been helped quite a lot as well, and I appreciate that help and tried to befriend the people who helped me (they all were classmates, and without the age factor), and I always failed.
These workmates of mine who are on their internship as well also believe I'm just lucky to know what I do instead of trying to ask me to increase their knowledge. They're free to do it. In fact, our mentor has recommended them to spend some time with me when I'm working. I've tried to help them many times but they just want my help when they need to finish something as soon as possible. So it's not surprise why I want to befriend someone who decides to help despite it's not his responsibility (like I said, this person is not my mentor. I'm not saying that my mentor is not doing his job properly, he just let me to seek for tasks from others) and who happens to be similar to me.
As you can see, I am someone who values people's knowledge and skills. And of course, I won't force anyone to meet in person because I value people's time, too. I hope this makes my situation much clearer and that my intentions aren't inappropriate or unusual from my perspective.