Reports claim Abramovich is considering firing Mourinho should they fail to win their game against Liverpool on Saturday.
But Remy is desperate for Mourinho to stay at the club, despite the Stamford Bridge side’s struggles so far this season.
Remy told the Evening Standard: “It’s important for him (Mourinho) to stay and we don’t want to give up.
“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.
“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.
“You could see against Stoke we played well, we created situations but we just didn’t score.
“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.
“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.”