As explained on the Xenopedia wikia:
Eggmorphing was originally to be witnessed during the climax of Alien,
when Ripley discovers Dallas and Brett cocooned in the Nostromo's
hold, with Brett being transformed into an Egg. The entire sequence
was cut as director Ridley Scott felt it slowed down the final act of
the film. However, the scene did appear in the movie's
novelization, and was referenced in the novelizations of the sequel
films.
As its source for this explanation, the wikia refers to The Alien Legacy:
The Alien Legacy is a 1999 making-of documentary directed by Michael
Matessino that details the production of the 1979 film Alien. Created
for the Alien Legacy DVD box set, it uses interviews with the film's
crew, as well as behind the scenes images and clips, to detail the
development, filming and release of the movie.
The relevant part is in the "Alien on Board" part:
The seventh and longest chapter goes into the filming of the titular
creature, in particular focussing on the infamous Chestburster scene
and the decision to show as little of the Alien as possible throughout
the film. Notably, the documentary also shows the deleted Eggmorphing
scene almost in its entirety.