at (one's) earliest convenience
As soon as one is able to do something. Please fill out that paperwork at your earliest convenience. Dan needs to call me at his earliest convenience.
at someone's earliest convenience
as soon as it is possible for someone to do something. (This is also a polite way of saying immediately.) Please stop by my office at your earliest convenience. Bill, please have the oil changed at your earliest convenience.
at your earliest conˈvenience
(written) as soon as possible: Please telephone at your earliest convenience.