Germany's most successful side are currently 11th in the Bundesliga table having drawn their first two matches in which they have lacked their usual spark.
"He will win games. The team is just coming together so we should give it and the coach some time," Bayern general director Karl-Heinz Rummenigge said on Thursday.
Van Gaal took over as coach this season with the brief of turning Bayern into champions again, capable of competing for the European Champions League crown.
So far they have looked unconvincing but the Mainz game provides them with an opportunity to set the record straight and close in on pace-setting Wolfsburg and Schalke 04.
"I dream of a van Gaal era that will last for many years and that will be sprinkled with titles," Rummenigge told Bild newspaper.
The coach has his work cut out with several teams looking strong enough to fight for the championship.
Champions Wolfsburg host Hamburg on Sunday.
Schalke coach Felix Magath has warned his players to keep their feet on the ground after going joint top of the Bundesliga following wins in their first two matches.
"I am happy that we have won but nothing more has happened yet," he said after their 3-0 win against VfL Bochum last week.
Magath led Wolfsburg to a surprise Bundesliga title last season and has also won back-to-back doubles with Bayern in the past. His side travel to Hoffenheim on Friday.
Underachievers Schalke have been in dreamland following a miserable campaign last season when all hopes of any silverware had evaporated by December.
Magath's championship instinct has already paid off with the emergence of teenagers Christoph Moritz and Levan Kenia.
"We can greatly improve and we want to get maximum points from every match and eventually win the title," said 18-year-old Kenia on Thursday.
"There is no specific target for this season but we want to win every game."
