I have just been offered a new job and would like to end my current notice period early, but this would require a buyout from my new employer. I want to ask my prospective employer for a buyout, but the employer has not mentioned anything about it during my interviews. Is it okay if I mail them asking for a buyout? How do I approach this?
the employer has not mentioned anything about the buyout during my interviews
This may be because they have no idea that you need/want a buyout. Unless this is common in your field or part of the world, there is a good chance they have no idea.
is it ok if I mail them asking for a buyout, or how do I approach this?
I would not do it via mail. Too impersonal. Talk to the hiring manager directly. Tell them the conditions of leaving your old employer, whatever they may be. Then mention the possibility of a buyout to change the conditions.
For example, say your current contract says that you must provide 4 weeks notice before leaving or reimburse the company $1k USD per week short of 4. Then ask your prospective employer if pushing off your start date 4 weeks to meet that obligation is okay. If they need you earlier, ask if they can provide some sort of a signing bonus or buyout to cover the expenses.
But, talk to the hiring manager directly about all this, either in person or over the phone. Then whatever the two of you agree too, make sure it is in writing in the contract you sign with them.