It might be that you are so desperate to get your ex back after the relationship fell apart, that you are even willing to stay just friends, so that you can at least see your ex from time to time.
Listen to me though - you are clutching at straws here because of your desperation, and it is definitely NOT a solution to your problem.
You see, if you tell your ex that your are willing to stay just friends, then you are offering yourself as a complete doormat to your ex.
What a pleasure! Your ex can date other people and go out and have loads of fun, while you sit around waiting for the times that your ex needs you as a friend.
In the meantime, you are sitting around at home getting more and more depressed because your ex is possibly getting involved with someone else.
This is just not on, so don't even suggest this to your ex.
Another thing, your ex is going to realize that you are making this offer because you are desperate, and he/she will lose all respect for you as well.
You will come across as a total loser to your ex.
I suggest that, before you make this offer to your ex, you take time to get over the break up first.
Once you are back to your old self again, you will be thinking a whole lot clearer, and you will realize then what a pathetic suggestion you could have made to your ex.
Don't sit around waiting to get your ex back.
Rather live a little, even though you will be without your ex.
Go out with your friends and have some fun - it'll help you get over the break up.
After a little while, if you still feel the same about your ex, then make contact and try to sort out your problems, without offering to be just friends - either you are in a relationship, or you aren't - that is all that you want.
Get your ex back on your terms.
If you are meant to be together, then it will happen naturally, you'll see.