The correct option is A Michael told John that he would be going to work the following week.
Direct speech is a sentence in which the actual words of the speaker are quoted.
Indirect speech is a sentence in where we report what someone said, without quoting his exact words.
In Future Continuous Tense 'will be' changes into 'would be'.
Here, option A is correct. 'Will be' changes into 'would be'. 'Said to' changes into 'told'. While, 'next week' changes into 'the following week'. Pronoun changes accordingly. 'I' changes into 'he' as Michael, the speaker was talking about himself.
In option B verb doesn't change. So, it is incorrect.
In option C pronoun is not changed. So, it is incorrect.
In option D verb is wrong. So, it is incorrect.