According to a survey published on the website ConservativeHome, Johnson is backed by less than one in 10 party members.
The survey comes after widespread speculation that Prime Minister Theresa May could soon be forced to resign as her popularity withers following her embarrassing election gamble, which left the Tory party short of a working majority in Parliament.
In the aftermath of the election in June, it was reported that a handful of ministers at cabinet level were pressuring Johnson to push himself forward to replace May.
The foreign secretary, however, dismissed suggestions that he was readying for a leadership contest as “tripe,” and instead gave May his full backing as she leads the country with a minority government.
Few of Johnson’s cabinet colleagues fare much better in the popularity stakes.
Not a single member of the government appears to have won the majority of party members’ support. The survey revealed that 34 percent want someone outside the establishment to become Britain’s next leader.
Although Brexit secretary David Davis is seen as the favorite among 11 contenders, he still only has the backing of just under 20 percent.
Johnson scored 9.5 percent, down almost 10 points since last month, while Chancellor Philip Hammond scored 5.4 percent. Home Secretary Amber Rudd lagged behind at 4.6 percent.