The usage completely depends on the situation. If you’re asking for the phone number right then, it should be can I have. If you’re asking whether there was a possibility at a previous time when you could have got the other person’s phone number, then it should be could I have.
There’s the difference between the two sentences. The question you’d probably want to ask sometimes could also be “May I have your phone number”
Modal auxiliary verbs ”can”or ‘could” perform different functions and can be used in sentences to express ability, permission, possibility etc whereas ‘can’ is used with less polite request like requesting a friend or colleague and mostly used for small things the auxiliary ‘could’ is used for making a polite request to someone who has a formal relation with you.
We can differentiate it in various ways
When you want to show it as a polite request.
Could I have your phone number?’ is better than saying ‘Can I have your phone number?’
See how we differentiate between ‘Can’ and ‘Could’-
Can I have your phone number?
- It is a casual sentence or it can also be called an informal sentence.
- There is no request in this sentence.
- There is no permission in it.
- The sentence with the word ‘Can’ express the ability.
- It shows a permission but it is better to use ‘May’ or ‘Could’ instead of ‘Can’.
Could I have your phone number?
- ‘Could’ is used in a formal sentence.
- It is used for a polite request.
- ‘Could’ is used as a past form of ‘Can’.