Queiroz's contract expires next month and reports have suggested that he could leave his role to take charge of South Africa for a second time.
The former Manchester United assistant manager and Real Madrid boss has been with Iran for three years and Dejagah is hopeful that he will remain in place beyond this summer's tournament in Brazil.
The Fulham winger said: "I hope Carlos stays with us - and qualifying for the next stage can help that.
"We will all benefit from his experience in the long-term."
Dejagah reckons Iran can be competitive in a World Cup group also containing Argentina, Bosnia-Herzegovina and Nigeria, although he accepts that a good start is vital.
They are 3/1 to beat Nigeria in their opener in the World Cup Betting and Dejagah said: "We have a good chance of reaching the next stage if we can beat Nigeria in our first game."