Notice period of 60 days and my last date would be 19 April 2020 and Lock down period is imposed till 14 April 2020

I have Submitted resignation to current company on 20 the feb 2020, for which i have to serve notice period of 60 days and my last date would be 19 April 2020.
As you know Lock down period is imposed till 14 April 2020 as expected.
Now New Company HR is Uncertain about my joining date as of now, in this situation, should i extend my notice period current company last date. is it possible to extend notice period. How should i tackle this situation . I dont want to be jobless.

Dear Gourav,
It is a little early to say anything at this stage. Though national lockdown may be lifted, the state government may continue with it depending on the situation that will prevail on 14th April. We do not know whether the lockdown in your city will continue or not.
Has your current company arranged your replacement? If yes, then they may not need you. However, if they could not get the replacement then possibly they may approach you for the extension of the notice period. Therefore, let the request come from them.
Thanks,
Dinesh Divekar