The Portuguese called Ranieri "a loser" when he replaced him at Chelsea during his first stint in England, and their relationship deteriorated further when they were both managing in Serie A.
Ranieri, who led rank outsiders Leicester to a title triumph last season, insisted the past was dead and buried and he was willing to share a glass of wine with Mourinho after the game.
"It's prehistoric," Ranieri told reporters at a news conference. "It was a long time ago. It's normal (now)... I love red wine, and if he offers I will go and drink it with him."
Mourinho's third stint in the English top flight has already seen a cessation of personal hostilities with Manchester City's Pep Guardiola and Watford's Walter Mazzarri.
Guardiola and Mourinho's relationship stretched to breaking point when they were in charge of Barcelona and Real Madrid respectively, while the Portuguese described Mazzarri as a hard-working donkey when the two were rivals in Italy.
United go into the Leicester game after suffering consecutive league defeats by City and Watford, but beat Ranieri's team the last time they met -- in the Community Shield in August.
Ranieri, whose team trail seventh-placed United by two points, also defended Mourinho's public criticism of his players in the wake of United's 3-1 defeat at Watford last Sunday.
"He is a great manager, intelligent and a fantastic person," Ranieri added.
"Every manager has his (rule) book and sometimes you need to do this (criticise)," he said.
"Sometimes, maybe not here, but at another team, also I push to provoke the reaction of the player. There's always a psychology."
