The Dutch manager is under pressure to save his job after his side were knocked out of the Champions League without a single win in the group stage, while they have been inconsistent domestically.
A further 2-1 loss against St Johnstone added to the pressure, though the Gers have since managed to get back to winning ways with a 1-0 win against Hearts.
McManus feels that though the Rangers fans voiced their displeasure following the loss to St Johnstone, the board will not take the drastic decision to sack Van Bronckhorst just yet.
However, yet another loss before the international break could put the 47-year-old under pressure, McManus believes.
“I think the board will continue to back him as long as he keeps winning games”, McManus said on PLZ Soccer.
“The two games before the break were vital.
“They got three points the other night, albeit not a vintage performance.
“And I think if they go and win at St Mirren, they stay just about in touch with the title race.
“They are still in both cups.
“So I think he will get an opportunity to see out until the end of the season.
“But obviously anything other than a win on Sunday, he is in trouble again.”
Rangers currently trail Celtic by seven points and may need to win to keep themselves alive in the race for the Scottish Premiership title.
