Could I call you?
1. I am too busy to talk to you now. Do you mind if I telephone you later on? (Usually in a business context. Also used with can in place of could. May is too polite here.) Sally: I can't talk to you right now. Could I call you? Tom: Sure, no problem. Bill: I've got to run. Sorry. Can I call you? Bob: No, I'm leaving town. I'll try to get in touch next week.
2. Do you mind if I call you and ask for another date sometime?; Do you mind if I call you sometime (in order to further our relationship)? (Usually in a romantic context. Also used with can or may in place of could.) Mary: I had a marvelous time, Bob. Bob: Me, too. Can I call you? Mary: Sure. Bob: I had a marvelous time, Mary. May I call you? Mary: Maybe in a week or two. I have a very busy week ahead. I'll call you, in fact.