Mourinho told Italian journalists that he doesn't think that his position is under threat due to the financial ramifications for the club.
The 55-year-old signed a new contract at Old Trafford in January and believes any potential pay-off would be enough to see him remain in charge of the Red Devils.
Manuel Pellegrini shares favouritism in the market with 888Sport also making the West Ham manager 3/1 (4.0) to be the first top-flight boss to leave their position.
The Hammers had high hopes coming into the new campaign. The London club invested over £100 million in the transfer market but that spending spree has had quite the opposite effect. West Ham have lost all four Premier League matches thus far leaving them bottom of the table.
Things are unlikely to get any easier for the former Manchester City boss following the international break. West Ham face Everton, Chelsea and Manchester United in their next three league matches and they'll be underdogs with the bookmakers in each of those clashes.
The West Ham board have usually been patient with their managers but a failure to register a single point - even with a tricky fixture list - means the odds compilers aren't taking any chances on an early exit.
Rafael Benitez is a 6/1 (7.0) chance having endured a frustrating few months at Newcastle United. The Magpies have only picked up one point so far and the Spaniard was unable to bring in the reinforcements that he would have liked during the transfer window.
Southampton secured up a much-needed win over Crystal Palace but Mark Hughes remains at 6/1 (7.0) alongside Neil Warnock although Cardiff's spirited performance against Arsenal is unlikely to have had too much of a negative impact on the Bluebirds' coach and his position.