In English when we report an imperative sentence or a request, we usually use a to-infinitive structure.
Examples sentences :
DIRECT SPEECH : "Can you open the door for me?"
REPORTED SPEECH : He asked me to open the door for him.
DIRECT SPEECH : "Could you help me with these bags?"
REPORTED SPEECH : She asked him to help her with her bags.
DIRECT SPEECH : "Can we have a meeting at 3 o'clock?"
REPORTED SPEECH : He asked them to have a meeting at 3 o'clock.
DIRECT SPEECH : "Can you look after my cat for the weekend?"
REPORTED SPEECH : She asked me to look after her cat for the weekend.
DIRECT SPEECH : "Could you turn the music down, please?"
REPORTED SPEECH : She asked me to turn the music down.
DIRECT SPEECH : "Would you like to go out for dinner?"
REPORTED SPEECH : He asked me to go out for dinner.
DIRECT SPEECH : "Would you like to stay for a coffee?"
REPORTED SPEECH : She asked him to stay for a coffee.
DIRECT SPEECH : "Can you clean your room, please?"
REPORTED SPEECH : She asked her to clean her room.