The London outfit have made a poor start to their Barclays Premier League title defence this season, collecting only four points from their opening five games of the campaign.
Saturday's 3-1 loss at Everton was a third defeat in four outings for Mourinho's men, who were beaten only three times in the league in the whole of last season, and t hey are already 11 points behind leaders Manchester City
But Tim Rolls, chair of the Chelsea Supporters Trust, is confident Mourinho will turn things around and does not expect a backlash against the Portuguese manager.
Asked if Chelsea fans still loved Mourinho as much as ever and wanted him to continue, Rolls told Press Association Sport: "Absolutely - you can look at social media and find one or two hot-heads, but most people know Mourinho is as good as it gets.
"We are only five games into the season and I wouldn't say it is a crisis.
"There are just problems that need sorting, and I'm confident Mourinho will do that.
"I think most supporters are fully behind him.
"It is important to maintain a sense of perspective, and I can't see any scenario in which anti-Mourinho chants would start from Chelsea fans at Stamford Bridge or at away games.
"I don't think he is under pressure, other than that he is putting himself under."
Rolls added: "(Chelsea owner) Roman Abramovich is in it for the long term.
"It finished quite sourly between him and Mourinho in 2007 (when the manager's first stint in charge ended) - I think everyone is now older and wiser and realises Mourinho is as good as it gets.
"In my mind it would be absolutely futile getting rid of him because I don't think there is anyone better who could come in - Mourinho is arguably the best coach in Europe."
Rolls can still see Mourinho guiding Chelsea to a successful 2015-16, despite the way it has started.
"The players who really fired last season like Eden Hazard and Diego Costa don't seem to be quite firing yet, and there are obviously some issues at the back too, but I'm sure all this will be resolved," Rolls said.
"I'm still very confident we will finish at the very least in the top three of the league.
"I'm not saying we will win the league from here, but I certainly think we still can - City will slip up at some point, so we'll see.
"And I would expect at least one good cup run, hopefully in the Champions League."
Source : PA
Source: PA