United have not lost any of their 10 matches since Ole Gunnar Solskjaer was appointed as Jose Mourinho's interim successor in December.
Solskjaer has earned acclaim for his impact on the team, moving away from the pragmatism which typified Mourinho's reign and bringing back more of an attacking style of play.
That has seen United charge back into contention for the Champions League spots, and they head into Saturday's trip to Fulham – who are in the relegation zone – just two points adrift of fourth-placed Chelsea.
In contrast, Fulham are seven points from safety and have won only once in their last five league games, but Ranieri does not think his team should be completely written off.
"We must be positive and have to fight," Ranieri told reporters. "If we don't fight and lose, you lose before you play.
"It's not tragedy, it's football. We used to fight. If the opponent is better, well done to them. I want to see my players fight until the end. My fans will be happy seeing the players fight for every ball.
"Sooner or later they [United] have to lose. Why not against us?"
While Ranieri is certain United's unbeaten run has an end date, he does feel Solskjaer is doing enough to land the job on a full-time basis.
"He deserves it at the moment," Ranieri said. "He shows the players are with him. Manchester has changed the mentality, why not?
"The result speaks for him. All victories and one draw, the players change their mind, more involved and they are fighting together."
Anthony Martial is enjoying a strong season for United and, although he caught the eye under Mourinho earlier this term, he has arguably found another gear since Solskjaer came in.
Ranieri knows him well after signing him for Monaco and is aware of the threat he will pose Fulham.
"I signed him for £5 million, it was good business," the Italian said. "He was very fantastic. I watched him during an under-22s match against Monaco [playing for Lyon] and was impressed.
"When the chance came to buy him, I said, 'Take this guy, because for me he could have a good future'. He came to Manchester and well done to him.
"He's very good. He can dribble, [he's] strong, fast. There are so many good players [in the United team] - [Paul] Pogba, [Marcus] Rashford, so many. We must be concentrated and strong, positive to show our personality during the game."