Grant's job as manager at Upton Park has been rife with speculation with the team at rock bottom in the Premier League, but a win against Birmingham City in the League Cup has installed some confidence within the Hammers' board.
A good run of form has also helped the former Chelsea and Portsmounth boss, losing only one of their last seven games, and Parker says that the team is fully committed to supporting the manager.
Asked if the players were united behind him, he replied: "Yes, definitely.
"The lads are fighting as much as the gaffer is fighting. We're all in the same corner.
"We're all trying to do our best for ourselves, for the manager, for the club. The manager's got tons and tons of experience and he's doing a good job."
Parker added: "If you believed everything you heard about this club, you'd be rather a stressed man.
"Avram's demeanour seems quite relaxed and chilled out and I think that filters down to the players.
"Obviously we're feeling positive. We have been on a run of good form, if you take the 5-0 defeat at Newcastle out of it.
"We have picked up some good results and we will go into the Arsenal game confident."