Rangers finished second in the Scottish Premiership this season as Neil Lennon guided Celtic to an eighth-consecutive league title.
Hoops fans are now keen to chase down the elusive ten titles in a row, but Van Bronckhorst reckons that two Rangers stars could halt their charge.
“Every side needs a blend and Rangers will have plenty of experience in Jermain Defoe and Steven Davis,” he told the Daily Record.
“The pair of them have had excellent careers and they are excellent professionals.”
Davis has been handed a one-year deal by Gerrard after impressing in the Rangers midfield after joining on loan from Southampton.
Defoe still has a year left on his loan from Bournemouth and could play a vital role if Alfredo Morelos leaves the club this summer.
Van Bronckhorst continued: “They will want to show they have plenty more left to offer and that’s why they will be crucial to any success Rangers are to have in the new season.
“Jermain still has the ability to score many goals and link play in the final third.
“Steven is very calm and stamps his authority in the middle of the park.
“Steven Gerrard will be counting on them to push all the way for the title. For a couple of years they were struggling to get close to Celtic’s level but that’s not the case now.
“They now have to take the positives of the two victories against Celtic last season and bring that mentality and skill over the course of a full campaign.”
Van Bronckhorst has warned Celtic boss Lennon that he will not have an easy ride next season, and that the gap between the Old Firm rivals is now minimal.
He told The Sunday Post: “Thanks to a lot of hard work behind the scenes, and the appointment of Steven Gerrard as manager, the club is now heading the right way.
“They are now very, very close to being at the same level on the park.
“Of course, it is an important period coming up, and they look as though they are ready to go and properly challenge.
“This will be a test for Celtic, because Rangers are ready.”