Mourinho, whose Chelsea side face Premier League leaders Liverpool at Anfield on Sunday, has always enjoyed a strong rivalry with the Merseyside club.
Liverpool manager Rodgers worked under Mourinho during the Portuguese's first stint at Chelsea in 2004-07.
The Northern Irishman believes, despite Mourinho's mind games, he has the utmost respect for Liverpool.
"There is no doubt that there was a period back in the early 2000s, that this club was a possibility for him," Rodgers said.
"Maybe resources were different and he had a better opportunity to go elsewhere but make no mistake, he knows the size and prestige of Liverpool.
"There has been a history there, what with the rivalry and it was a great rivalry between the clubs, but beneath it all he knows the power of Liverpool for sure."
Mourinho was reportedly close to taking over at Anfield in 2004, when Gerard Houllier was being replaced.
Rodgers said Mourinho urged him to take the job at Liverpool when it became available in mid-2012.
"He told me to take the job and what a great club Liverpool was. I had spoken to him about it, he encouraged me about the sheer scale of the club," Rodgers said.
"I was talking to him about a choice I maybe had, but he knows the size of this club. I understand full well the Liverpool-Chelsea rivalry and in that period maybe it was the managers and that was the rivalry.
"But for me there is no drama, no issue with him. The advantage I have is I know Jose behind the manager, a man who is humble, respectful, has real good values and ethics, but he is a winner and he wants to win.
"And I know even if we are considered a rival that if they didn't win the league he would want Liverpool to win it."
