How to get the notice period reduced?

So I interviewed with a company two months ago, after all the formalities were done, I received a response from the HR that I have cleared all the rounds. But the requirements for the position they were hiring me for suddenly changed and they asked me to wait for a while until a new position positions opens up matching my tech stack. At that time I was about to be released from a project in my current company so getting the notice period reduced to 2 months was not that much of a hassle. Today, the HR called me again telling me that a new position has been opened up and if I am available to join I can join. My official period is of 90 days and now I have been allocated to a new project in my current company. I have been wanting to switch since so long because of variety of reasons. But the problem now is the notice period in my current company. The HR is very strict about joining within the 60 days but I am not getting any vibe that my current manager is going to reduce my notice period.

Please suggest if there are any ways out of it.

Thanks in advance!!