Welcome to English Language and Usage or English.StackExchange.com, also called English.SE, EL&U or ELU. As a new member you cannot be expected by anybody to be an expert at knowing how to ask a question here, but please be informed that questions of the type "is this sentence all right" or "is this phrase all right in this sentence" are considered 'proofreading' here, which is a reason to close a question as off-topic.
As the close notice explains, "requests for proofreading are off-topic unless you have raised some specific concern with the text" (paraphrase). Since it would be interpreted as 'proofreading', a member cannot simply suggest a phrase and ask whether it is grammatically correct.
So what does the community expect?
Taking your own question as a specific example, the first thing expected is that you must explain why you have the idea that 'would you have interest' might possibly be grammatically incorrect. Also, what alternative phrase have you considered?
[It's probably not enough to say, "my friend says it is incorrect." Why does your friend say so? We expect you to find that out and specify it in your question, which you can edit and improve before submitting for reopening, right here on meta.]
Secondly, and whatever be the nature of any member's question, they need to show what research they have done by themself on this question before asking it here at ELU. Not showing research is itself a reason to close a question. It is also very useful to provide an example sentence to show us how you plan to use the phrase in question. All of that demonstrates that you have a genuine and specific problem with syntax, grammar or usage that persists even after you did your basic research, and also tells us what sort of solution you are looking for here.
To conclude, this is my suggested outline (not for copying but just to give you an illustration to work on) how the same question might be written in a way that is not a request for proofreading:
I need to write a recruitment notice and am having some difficulty with the expression 'would you have interest.' My friend says it sounds grammatically incorrect.
She is no expert and couldn't explain why, but I looked up the usage of the word "interest" online and found the following explanations of how it is usually used:
[please give extracts of definitions, usage notes and examples, with links to the websites that gave the information.]
I now have a specific concern whether 'have interest' is the right expression in this situation, as in
"would you have interest in taking up this project that pays three thousand dollars for three months' work and guarantees plenty of quality experience?"
My friend thinks that is not how native speakers of English would naturally use 'interest' here. I have considered alternative formulations such as "would you express interest", "will you be interested" and "would you show interest" but do not understand which is the best choice for this case.
So is 'would you have interest' the most natural expression in this context? If not, please explain why and also tell me which way 'interest' could be best used here.
Update: Nice to see your question reopened @Amber & I am quite sure (as also confirmed by the senior member Sven Yargs in the earlier comment here) that using "would you have interest in this job" is grammatically correct, although "would you be interested in" might be the more natural expression for native speakers of English, as noted in the simple yet excellent answer to your question, written by Jack Woods.
I am not a native speaker of English myself and we routinely use "would you have interest" in Indian English. Nobody will misunderstand your phrase and it is absolutely fine to use either variant.
I also particularly appreciate your willingness and effort to improve your question substantially based on community expectations, which convinced the members very much and succeeded in getting it reopened.