Ranieri, back in the English top flight for the first time since parting ways with Leicester City in 2017 having taken them to a fairytale title, said Mourinho was the first manager to welcome him back.
"He was the first who sent me a message to say welcome back. He is a very friendly friend. He told me, 'welcome back, all the best'. We speak about everything," Ranieri told reporters.
"It was a text message. Sometimes we speak. He's a fantastic man. I know him for a long time, when he came to Chelsea and in Italy, and he was very polite with me. He's a great man, coach, manager and also the football is important."
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Mourinho wore Ranieri's initials following his sacking by Leicester last year, a mark of respect to the man who nine months earlier had taken them to the title.
The Portuguese is having a difficult time at Old Trafford with the Reds in eighth place -- 18 points behind Premier League leaders Manchester City and eight off the top four.
Ranieri believes they are improving although he will be hoping to add to Mourinho's woes at the weekend.
"I think Manchester United are getting better," he said. "For us, it will be difficult. We have to make a perfect performance. Manchester United are one of the best teams in the Premier League, also in the Champions League they made a very good job. It's a fantastic team, a fantastic team.
"We want to make a point there. We know it's hard but nothing is impossible."
Basement side Fulham have nine points from 15 matches and Ranieri said a string of good results starting with the game at Old Trafford could turn their season around.
"We are a work in progress. Last night, one point is much better than nothing," Ranieri said of Wednesday's draw with Leicester. "It's not easy, because when you stay at the bottom of the table, it's hard for confidence to be 100 percent.
"But if you get a couple of results, the confidence improves immediately, and I believe we can do this soon."
Ranieri enjoyed a winning start as Fulham beat Southampton 3-2 last month. But they crashed to a 2-0 defeat at Chelsea before the 1-1 draw at home to Leicester.
"I think if you observe the three matches, we improved a little more, a little more, a little more," Ranieri said.
"There is a lot more work to do, but we're in a good way."
Mourinho's United have drawn three consecutive Premier League games, twice coming from a goal down in Wednesday's 2-2 draw at home to in-form Arsenal.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Martyn Herman)
