Rodgers was one of Mourinho's former pupils at Chelsea, having worked under the Portuguese before embarking on his own managerial career.
The pair, who remained friends, go head to head on Sunday at Stamford Bridge.
Mourinho said: "We speak about basic things, 'Good luck', 'Well done', 'How's family?', 'Happy Christmas'.
"He was always a very open guy, open to learn, open to give his opinion, very interested in the game. We like him very much, me and my staff, we liked him very much since he started working with us.
"He's at one of the top clubs in England, one of the top clubs in the world. His ambitions now are to win titles at a big club."
During Mourinho's first spell, Chelsea and Liverpool were involved in some titanic tussles, particularly in cup and European competitions.
Mourinho and Rafael Benitez, who the Portuguese succeeded at Chelsea this summer, had an intense rivalry which peaked around Luis Garcia's 'ghost' goal, which helped to take Liverpool to the 2005 Champions League final, won by the Reds.
"You only have rivalries with big clubs, you don't have rivalries with small clubs, and Liverpool is a big club," Mourinho said.
"They were fighting with us for titles, for Champions League semi-finals, for cup finals, so it's normal.
"But at the same time I'm full of respect for Liverpool as a club, for Liverpool's history. I always had that and I haven't changed that because I am at a rival club."
Asked if Liverpool are now as good as they were then, Mourinho said: "They were a good team but they are building a good team now, too. I like their team."
Mourinho says that to beat the Reds on Sunday, they will have to be more ruthless in front of goal.
"For Chelsea to beat Liverpool, we need to score more goals with less chances," he said.
"Normally you don't create against Liverpool five or six or seven big chances. You get two or three and you need to score. We need to score more."