There's no specific date yet, all we can read now is just predictions as to when and where the right will happen.
This article says it could be this May or June this year, well, at least we will not have to wait longer if indeed it will be realized between that period.
https://talksport.com/sport/boxing/821324/frank-warren-prediction-anthony-joshua-vs-tyson-fury-may-when-june-heavyweights/
This is a big fight, probably the biggest this year, so promoters will ensure a crowd is possible, and it's not likely to take place in the US.
Maybe they are still undecided in terms of venue and date, as they want to attract live audience as much as possible.
So maybe they are checking the community about this covid vaccine. Once this is rolled-out in greater scale, that's when they can ensure at least live audience will be present.
They are still cooking the details and of course, know about the pulse of the boxing community.
This will be another money-maker for them. So they need to be meticulous with the details here.
The announcement by Fury might be accurate, he announce it early so he can sell the fight. These two are guaranteed to receive big money as this is a big fight that everyone wants to see. Of course, the venue is pretty much considered here and Bob Arum would ensure to make revenue on the gate entrance and they'll find a good location for that.
If this fight will be a controversial fight, people will be more excited to see a rematch, another money making opportunity.