The Bantams were held to a 0-0 draw by Yorkshire rivals Doncaster Rovers on a frustrating opening-day at Valley Parade.
Oliver was given little by way of quality crosses to feed off as Rovers defended stoutly against Mark Hughes's side.
The 30-year-old scored nine goals and provided four assists in 39 appearances for Gillingham in League One last term and Morrison feels he could thrive under Hughes.
"He [Hughes] has to get a tune out of those players, they've brought in Vadaine Oliver who scored a lot of goals for Gillingham in League One," Morrison told OLBG.com.
"I know they got relegated, but he's someone who will score goals for them. Bradford have got some talented individuals mixed in with Mark Hughes who is an experienced Premier League manager.
"There's a reason he went to Bradford, he probably felt it was a good project to go into and last season was his bedding in season.
"This season he has to try and get them promoted because Bradford City are a huge football club. They shouldn't be in that league, but no one has a divine right to get out of the league because there's a lot of good teams in there.
"They need to work hard, and I think they'll have a chance this season at finishing in that top seven places. When you've got experience with Mark Hughes and players wanting to come to Bradford to prove a point, then it bodes well for a good season.