The Israeli takes his side to Birmingham on Saturday, fresh from being told by David Gold that his job would be safe even if the club were to be relegated this season.
And although he admitted to not being happy about the current situation he finds himself in, Grant is content that he has the support of his employers, and believes they need to try and replicate the stability of Arsenal, who have had the same manager for 14 years, if they are to succeed.
"When people say bad things you ask me if I am worried and when people say nice things you ask me if I am worried too," he said.
"I am concentrating on my job, I need to do my job. We (him and the owners) share the same vision for the club and, as clubs like Arsenal show, you need to stick in the vision of the club in the good days and in the bad days.
"Today I cannot tell you we are happy about being at the bottom of the league but this is only temporary."
Form is not on United's side as they head to Birmingham, with Grant's men having failed to win away from home in their last 23 league games.
And although Grant accepts Alex McLeish's side represent tough opposition on home soil, he is confident his players can return to London with a positive result.
"It's difficult to play not only against the opponents but also against the statistics," he said. "But statistics are just statistics.
"One of the things we have to do is take it as a challenge and we are doing that. I am sure that we will win away games. I hope that happens at Birmingham and we will do everything for that.
"But Birmingham are a very good team and they are very good when they play at home. But this is football, so we need to think positive and anything can happen."
Battling midfielder Mark Noble will be missing for United due to having an appendix operation, while Julien Faubert is suspended and Jack Collison, Thomas Hitzlsperger and Tal Ben Haim are also injured.
England defender Matthew Upson could return from a hamstring injury, though, and Grant is hopeful that the 31-year-old will soon be penning a new deal at Upton Park.
The former Arsenal man's contract runs out at the end of the season and Grant would like him to extend his four-year stay in east London.
"For me what matters is if he is doing his job or not," he said. "Except in the beginning, he has has been going his job well in the last games that he played.
"Unfortunately he has been injured lately but what matters is if he is doing his job. The other things are normal, there are always negotiations between players and clubs, but I hope everything will be okay."