回复：回复：回复：回复：I wouldn't write such an email...

In that case, just use the opportunity to introduce your background and strength to the big boss, i.e. skills, experiences, knowledge, achievement, etc. without mentioning the new position in particular. (He needs to know you better, and, if he ever considers promoting you, you two need to feel more comfortable communicating with each other directly). It'll be up to him to 'think and decide' if you are not person...

It worth trying, and it is at least a good learning experience.