I would not mind anyone asking... But unless I felt confident that that person would fly and look after my pride and joy at least as well as I do, and make it worth my while, I would probably politely decline. I had a guy approach me that way recently but (1)he was looking for a significant saving over what a local flying school would charge for a scruffy similar age and model with much higher time and (2) he seemed to think I was something like Hertz car rental. Although he flew OK, he just did not display any kind of 'emotional' inclination to MY aircraft. I was not convinced he would look after it the way I'd expect as soon as he was out of sight. It was obviously just another hire to him. So I quoted him a rate higher than the local club... and off he went.
I guess the best advice is work on building a trusting relationship with an owner and who knows what you could achieve...