Try this
- Name the whole task, including preparation and follow-up, so the request is not smaller in wording than in practice.
- Wait for a clear acceptance. If the person declines or cannot answer, retain responsibility while choosing another plan.
A worked example
“Could you handle the reservation, or should I do it?”
An invented example to adapt, not a real exchange or a script you have to follow.
Before you leave it here
Wait for an actual answer before treating the task as transferred.