Yes
1-Paramount Pictures wants to make GF4 with or without Francis Ford Coppola.
2-There is a scrpit written by Mario Puzo in PP
3-Al Pacino told Coppola he would do whatever he wants him to do(Talking about a possible GF4)
4-Andy García wants a GF4
5-Mario Puzo obviously wanted a GF4 that`s why he sent the GF4 script to Paramount Pictures.