First go through your appointment letter. What conditions are mentioned in it for leaving the company.If there is no such conditions in your appointment letter, you can definitely buy your notice period. Give them reference of your appointment letter.
If there weren't any such declaration, you still need to refer the employment agreement. There must be a conditional statement made under the topic 'Separation'. What is it ? If they are ready to buy the notice period , why are you not considering it?
Serve one month and buy the rest of the duration. Speak to your future employer , if they can help you with the separation , in terms of offering a date within the duration and the documents you may need.
If the employer really needs you to join early, they can even offer you a joining bonus , which might be an equivalent amount to the notice period buy-out. Ask the hiring manager about it, once you are offered the role.
Looking forward to hear from you
Notice period is mentioned in the employment contract to avoid the loss employer and employee will bear of sudden termination.
If you have a clause mention to buy the notice period then buy the part of notice pay and rest you serve. Most of the time future employer pays on your behalf. For me company has paid when I resigned from the previous company. The same you can negotiate with your prospect employer.
The best thing discuss with your HR team whom you like the most and hope you will find a way to this issue.
Hope this may help you; I have seen Ms.(Cite Contribution) post and she has guided you in a right way.