1) You are putting it on me to tell you that I need something, right in the middle of my need. 2) If you're my real friend you don't need to say that, I already know I can call you 24/7/365 3) Your willingness to help is nulled by your lack of initiative.
The best thing anyone ever did was call me and say "I'm at Costco. What do you need? And don't say 'nothing'. I'm going to bring you something, and that's that." That whole pizza and frozen burritos were bad for me, but the last thing I needed on my mind at that time was cooking. And that's what true friends are there for.
So don't say "If you need anything let me know!" It's borderline passive aggressive.
@geocrasher seems to not realize that the people around he/she could be taking a cautious position to avoid getting into his/her business without it being requested.
I understand your point and i know it's a difficult question to deal with sometimes, especially during depression.
But remember that you're not those people's top priority. That sentence means you are allowed to ask them for stuff, but it doesn't mean they're going to drop everything and take you into their care right now without you taking a few steps on your own. They consider that you have enough of your own agency.
Your willingness to be helped is nulled by that same lack of initiative on your part.
A trick is to find something easy to ask for, as a go-to response to that. For example, the next time someone says that to you, you could answer:
"Actually, life has been tough lately, a beer would be nice".
What would have been better? To just say "I'm sorry you're having a hard time". If you don't mean something, don't say it.
I would like to be told by a friend that they care about me and would like to help in some way if they can. What I wouldn't like is if they said "OK, I'm going to choose a thing that I think I would want in your situation and do it for you, and you have no choice because I'm going to do it anyway." Chances are, what you thought was helpful is NOT what I need in a difficult moment and I don't want to be subjected to another person's choices being superimposed on my situation. Lucky for me I know that my friend feels the same way, and we have different ways of approaching these things with each other because of it.
"I'm at Costco. What do you need? And don't say 'nothing'. I'm going to bring you something, and that's that" seems incredibly aggressive to me, and if I had many friends who behaved that way I would be endlessly frustrated.