The embattled Portuguese coach has endured a torrid campaign with the Blues, and seven defeats from 12 games see the Premier League champions marooned down in 16th in the table, with league leaders Manchester City a massive 15 points ahead of Mourinho's men.
Chelsea are also out of the League Cup, having exited on penalties to Stoke City last month, and Mourinho is arguably under the most intense pressure of his career with the Blues.
The champions have suffered from a bizarre loss of form from several key members of last season's title-winning squad, with the likes of Cesc Fabregas, Nemanja Matic, Branislav Ivanovic, Eden Hazard and Diego Costa all way below par this term.
Chelsea felt compelled to release a statement to publicly back Mourinho after the defeat to Southampton last month, but results and performances have continued to nose-dive since the 3-1 reverse to the Saints on October 3.
Sky Sports published the statement: "The club wants to make it clear that Jose continues to have our full support. As Jose has said himself, results have not been good enough and the team's performances must improve."
Despite the continued struggle to find form, Wilkins, who was assistant at Stamford Bridge from 2008-2010 after a stint in the same role in the late 90s, thinks that Mourinho will stay in charge for the remainder of the campaign.
"Jose Mourinho will complete the season at Chelsea with no problem whatsoever," he told BT Sport. "Mourinho, for me, is far and away the best guy for the job."
Chelsea return to action after the international break when they host Norwich City on Saturday November 21, looking to end a run of three straight Premier League defeats.