Novak Djokovic is likely to lose his number one rank ahead of Roland Garros next week following the Italian Open as he's the defending champion with a lot of points there.
Djokovic will be only a handful of points ahead of Alcaraz if the Spaniard successfully defends him trophy which is expected. If that happens, Djokovic will likely lose his number-one rank next week because Alcaraz would only need to win two or three matches at the Italian Open in order to earn enough points to dethrone Djokovic regardless of how he does.
The Serbian is the defending champion so he can't really earn any new points and he'll lose a good amount if he doesn't defend his trophy. Having not played in a while, Djokovic doesn't seem like a good bet to make the final let alone with the trophy so it's safe to assume that Alcaraz will probably replace him at the top.
There is a minor chance Djokovic hangs onto it ahead of Roland Garros but that can only happen if Alcaraz doesn't play at the event like last year. It's widely expected that he will.