City, who play at Arsenal in the Saturday Night Football this weekend, are currently three points behind the leaders Chelsea, and two behind Liverpool.
They have two games in hand and a superior goal difference but Kolarov insists Mourinho and Rodgers both think differently in private, to what they say in public.
"It is my opinion, but they are in first and second place at this moment. They want to know that they are there for the title and they just want to put pressure on us," he told Sky Sports News Weekend Warm-up.
"They are fighting every game for the title and maybe now they have to admit that they are there.
"We know that they are trying to put pressure on us but we are used to playing with pressure because we have had it from the first game of the season.
"We wanted to win the title, this was always out target. They are now in the positions they are in, so they are both there for the title."
You can catch the full fascinating interview with Kolarov on Sky Sports News weekend warm-up from 18.00 on Friday