United travel to Stamford Bridge for the quarter-final tie five months on from their humiliating 4-0 Premier League loss to Chelsea earlier this season, a game in which the Belgium international scored.
Hazard, though, says he always felt Mourinho's men would come on strong as the season progressed and praised the quality of the Old Trafford club.
"One month ago I told people that I thought United will be the best team in the second half of the season,” he told The Telegraph. “Because they started slow, and then they have great players, a great manager, and they know what to do.
"OK, sometimes at home, they have lost some games or drawn, but they are in a good form. They had a long trip [to Rostov]. I expect a good game from them. They want revenge because we won at home 4-0 in the league.
"I've never won the FA Cup so I want to win it. It’s the oldest cup so I know for the fans it’s really important, for the players also because in the last 10 years Chelsea have won it four times.
“So now it’s in the minds of the fans that something can happen. So we have to win this cup.”
Chelsea currently sit 10 points clear at the top of the Premier League, having recovered from a dismal last season and a small run of bad results early in the current campaign. But Hazard feels it has been a new Chelsea team ever since they held a frank discussion after losing at home to Liverpool around that period.
"After we lost to Liverpool in September, we were worried," added the winger. "But we talked. The manager was not going to let that happen.
"He changed things. We said, 'We are Chelsea, we have to be at the top, now stop talking, talk on the pitch, win games'. And we did that.
"All of us have had more motivation this year, because you don't want things to be the same as last season. You want to be better. You know you are a better player than last season, so you know you have to do better.
"We have all had something to prove. When you play a bad game, next game you have to prove that the bad game was a mistake."