Media reports have speculated that the Portuguese could be dismissed by club owner Roman Abramovich for the second time if Chelsea suffer a sixth defeat in the opening 11 Premier League games.
He was sacked early on in the 2007-08 season before returning in June 2013.
Chelsea, champions last season, were eliminated from the Capital One Cup on penalties by Stoke City in midweek and have now won only one of the last seven games in all competitions.
In addition, Mourinho has been in trouble again with the football authorities. He is due to hear the result later on Friday of his appeal against a £50,000 ($76,680.00) fine and suspended stadium ban for comments about the referee after losing to Southampton earlier this month.
And last Saturday he was sent to the stands after allegedly insulting the referee during Chelsea's 2-1 loss to West Ham United.
Speaking at a news conference ahead of the Liverpool game, Mourinho said he was "not optimistic, not pessimistic," about the outcome of the appeal.
Asked about any discussions on his future with the owner, he refused to comment.
He did admit, however, that he cannot guarantee finishing in the top four to qualify for next season's Champions League, which some observers believe to be a minimum requirement to keep his job.
"I cannot promise," Mourinho said, pointing out that clubs as big as Manchester United and Liverpool had both failed in recent seasons to make the top four, and even finished outside the top six.
The champions go into the Liverpool game in the bottom six, although they are only three points behind Juergen Klopp's team.
"A guy I like a lot," he said of Klopp. "His work speaks (for itself) and I consider him one of the top managers in Europe."
Striker Diego Costa and fellow Spanish international Pedro will have further fitness checks before the game, when Mourinho is not expecting any great changes from the Liverpool of Brendan Rodgers, whom he once employed at Chelsea.
"They were a good team and they are a good team," he said.
"They had a good manager and they have a good manager.
"They change some details in the tactical approach but that's the nature of the game."
(Reporting by Steve Tongue; Editing by Rex Gowar)
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