Real go into the match on the back of two wins over arch-rivals Barcelona but Alonso insists United's good form - they have not lost in any competition since a Champions League dead rubber against Cluj on December 5 - more than cancels that out.
"We've enjoyed two day's decent rest (since defeating Barca 2-1 on Saturday) but both teams go into the game in decent form," he said.
"I think independent of what has happened in the last week in the two different competitions (Copa del Rey and league) we are coming into the game in good form and so are Manchester United.
"It is a very open tie, we come here knowing we need to score and they know they have to defend properly, but it will be very tight and close to call.
"It is a massive game and will be decisive in both teams' seasons."
Alonso - once a north-west rival of United when he was playing for Liverpool - counts his lucky stars Cristiano Ronaldo will be wearing white on Tuesday and is not still in the red of United.
"He is looking forward to it because it is a very important game against United," said the Spain international.
"Before the game I am sure he will get a great reception but on his mind is just to play a good game and get through this stage.
"Once we kick-off everyone will be thinking about doing the best for our team.
"It is very different playing against him (Ronaldo) than it is playing with him and I am lucky he is on my side, and I prefer to have him on my side.
"He is in terrific form at the moment. He has been very decisive in many important games and he that is what we are looking for tomorrow [Tuesday]."
Mourinho's reign at the Bernabeu seems set to end this summer and even winning the Champions League is unlikely to change that.
So do the players feel the manager's fate is in their hands?
"We are just focused on the actual result of the game and giving a good account of ourselves for 90 minutes - any repercussions beyond that have not entered our head at all," he said.
During the press conference a fan had to be ejected after interrupting proceedings by asking Mourinho if he was going to be the next Pope.
United's security team had been aware the man had gained access and had made the decision not to intercede until after proceedings had finished, but when he shouted out he was removed peacefully.