Can you say: did you mean x, instead? it would sound better. You could say you didn't understand him.

Are you friendly with this coworker?

@JasonJ Kind of. It's not something you can correct like that. For example, instead of saying "that", he says "this one". To be honest it's just me being a nit picking brit.

Are you sure your correction is grammatically correct, and that your colleagues speech is incorrect? Or is it just that his speech patterns annoy you? Sometimes non-native speakers can latch onto grammatically correct but uncommon patterns because they have no clue.

What does it have to do with native vs. non-native? It's either right or wrong. If it is done with the intention to improve things, it's fine. Unless the person complains; in that case it's the end of free English lessons. Please please please make sure that any corrections are actually correct!

@PeterM It definitely doesn't sound correct, an example would be pointing at a whiteboard across the room and saying "Can I write something on this one?", instead of "Can I wrote something on that?"..

In that case he is technically wrong.

Non native speaker here. FWIW, I love it and I'm very grateful when (at least people who I interact with reasonably frequently, not the teller at the bank) correct even the slightest mistake or slightly weird-sounding sentence I come up with. I appreciate pronunciation tips - with one exception: don't try to make me sound more American, my life's ambition is eventually sounding like John Cleese on Fawlty Towers :)

He'll only know that he's using it incorrectly if he is told. With my second language, I appreciate any correction when I speak incorrectly because you get to a point where you just have to speak the language a lot to practise. If no one says anything then you just don't know until one day you realise that you've been doing something wrong the entire time and no one told you. Then you're like why didn't anyone tell me?!?.

@SeanBean If that's the kind of thing 'this one' vs. 'that', I would not. That correction is hopelessly pedantic.

Have you asked them if they want to be corrected in this manner? If they have just a short assignment that needs English, perhaps they don't want to take the time to learn what is correct. If they state they do want to be corrected, you have an open invitation to correct whenever (and just about however) you want.

There exists a saying, Praise in public, coach/criticize in private. The only thing that the saying does not cover is that YOU must remain absolutely open-minded when in private and approach with utmost humility and show that this conversation is not an easy one. Do not be steadfast.

Can you provide examples? Or even a general sense of the type of errors he's making? From the information you've provided, it's not clear if you're talking about nitpicky grammatical corrections or linguistic errors that could actually effect the meaning of what he's saying, or something in between, and that matters.

I see a lot of answers saying you should say this or that instead of what you are proposing. Yes, correct them. But use your own words, not everyone else's.

Can you explain the context where you are going to make corrections? For example, if your colleague is explaining something in a meeting, and you respond by correcting his grammar, that is one thing (don't do this unless the correction is necessary for understanding). On the other hand, if your colleague has written something unclear in written documentation, that is another.

@SeanBean "Can I write something on this one?", instead of "Can I wrote something on that?" Given those two choices, the first one sounds more correct to me. Saying 'Can I wrote something...' is quite confusing with the past tense (did he already write it, or is he going to?). On the other hand, saying "this one" instead of "that one over there" sounds like an idiosyncracy (i.e. when he says 'this one' you know it's his own special way of saying 'that one').

Apart from the already posted answers, context is very important. It is not the same correcting someone when he is speaking directly to you when he is talking to a group of twenty people. It is not the same if the conversation is casual or serious. It is not the same if you already know each other or if you just met....

As a non-native English speaker, I'm grateful when my mistakes are corrected. That said, many Spanish speakers (and from Spain in particular) are notorious for not caring much about other languages' rules and uses. (My source: a life of 50 years as a Spanish speaker).

@TobiaTesan If you think about it, everyone is a non-native speaker of almost every language. :-)

As a non-native English speaker who speaks five languages, I don't find it particularly attention-worthy, let alone offensive, if someone corrects me in one of them, especially when that one language is probably the only one he knows. ;-) I just accept the correction, thank him, and move on.

I would prefer to be corrected. Then I'll not repeat the mistake.