The People says speculation is growing former Blackburn and Wales boss Hughes is under threat from unhappy Abu Dhabi based billionaire owner Sheikh Mansour bin Zayed Al Nahyan.
The 45-year-old City manager will fly to the Middle East for his first face-to-face sit-down with his wealthy boss on Wednesday.
Hughes said: "No one is immune from the sack. But all we are trying to do is build a club and it won't happen overnight. The team finished eighth last year and we want to be better than that this year - hopefully we will.
"The owners are very calm about things and I don't think they are the types to have a knee-jerk reaction to bad results.
"Everyone else is a bit hysterical about what we are trying to do and putting expectations on us even before we have the benefit of going into the market to get the players that we obviously need.
"This is a long-term project and the owners understand the team isn't going to be challenging immediately.
"Their aim is that sometime in the future we will be challenging for the top honours but it won't happen after the events of one day in the transfer window when we bought Robinho. The owners are realistic in their aspirations and haven't set me any targets.
"They are not here for short-term gain, they are here for a long period."
There is no suggestion bad news is imminent for Hughes, though yesterday's defeat to Tottenham will increase pressure.