Despite winning the title last season, Mourinho's position is coming under increased scrutiny following a poor start to the campaign which has seen them lose half of their opening 10 league fixtures.
Having also lost their Capital One Cup fourth-round tie to Stoke on penalties on Tuesday, the Portuguese is likely to come in for more criticism and cracks have begun to appear in his usually cool demeanour.
He has hit out at the media and snubbed all post-match press duties following Saturday's defeat at West Ham, while he faces a Football Association charge having been sent off following a half-time altercation with referee Jon Moss at Upton Park.
But, despite different reports surfacing that claim a number of senior players at Chelsea want Mourinho to go, Remy - who scored the late equaliser at the Britannia Stadium that saw their cup tie go to penalties - told the London Evening Standard that the boss still has the backing of the dressing room.
"It's important for him to stay and we don't want to give up," the forward said of Mourinho.
"We were champions together only last season and he is a really great manager
Of course I don't want him to leave
I think all the players don't want that.
"The spirit is good and we are not affected by the situation
We will just keep training well
I'm sure the opportunity to win games will be here sooner rather than later, but obviously it is better for us if it is sooner."
Chelsea host Liverpool on Saturday as Mourinho comes up against Jurgen Klopp - who replaced Brendan Rodgers following the Reds' own indifferent start.
Remy admits the fixture is a big one but the France international has also backed Chelsea to finish in the Premier League top four despite currently languishing down in 15th - nine points adrift of fourth-placed Manchester United.
"I'm really sure that Saturday will be a big game, but we can still be in the top four of the League if we win games," he added.
"It does look and feel like, after losing on penalties, that things aren't going our way
But when you know the quality of the group and the fact we were were champions last season, which was not by chance, the quality is still here."
Remy has started just one Premier League game so far this season but is in the frame to line up against Liverpool after Diego Costa was taken to hospital following a rib injury that forced him off after 32 minutes at Stoke.
Source : PA