Fill in the blank with the most appropriate word.
________ have a cup of coffee if you don't mind.
The context indicates
a preferred choice. Thus, the phrase 'I'd rather' in option C, which is a
contraction of 'I would rather' is correct because if you say that you would rather do something or you'd rather do it, it shows you preference to do it.
Option A informs of a decision, but this is incorrect as the sentence also
refers to 'don't mind', which implies apoliterequestordesiretomakesuresomeonedoesn't object.
Option B is incorrect as it is not in agreement with the phrase 'if you don't mind'.
Option D is incorrect as the verb 'prefer' will take a to infinitive.
Thus, option C is the correct answer.