United are currently on a five-game winning streak in the Premier League which has seen them beat Chelsea, Liverpool and Manchester City – denying the latter the title by coming from 2-0 down at half-time to win 3-2 last weekend.
But complacency cannot be allowed to creep in for United as they look to secure second place even though West Brom have won just three of 33 matches all season and are 12 points from safety.
West Brom appeared on course for a long-awaited win last time out in their first game under caretaker boss Darren Moore but threw away a lead to draw with fellow strugglers Swansea.
The Red Devils, meanwhile, are just one point above third-placed Liverpool, although they still have another game in hand after facing the Baggies today.
And Mourinho – who has a fully-fit squad bar injured back-up goalkeeper Sergio Romero – insists his side must be prepared for a challenge against the West Midlands outfit at Old Trafford even though the visitors are winless in 15 top-flight outings.
“I think [it we will face] a big challenge because they know that in football anything is possible until mathematically it is possible. They know that,” Mourinho said.
“Everybody knows, they know and they still smell a chance, but every match that is played, if they don’t get points, then they are closer to relegation. I think they still believe that mathematically it’s possible.
“The quality, the experience of many of the players, the squad, the stability of the past years, it is a surprise for me that they find themselves in this position.”
United have received criticism throughout the campaign for their sometimes negative style, but Mourinho recently declared that his side deserve to finish second behind neighbours City.
And the Portuguese boss, whose side have the joint-best defensive record in the league, insists there is still work to do to finish above rivals Liverpool.
“In our case, we come from a big result,” the United manager added.
“During the week I was trying to fight that result by working well and hard and trying to make the players understand that it’s not enough to deserve to finish second, we need the points to finish second.
“Obviously to finish top four we need four or five points. But to finish second we need much more than that.
“After three important points last weekend we have to try to do this three and be closer to the end of the season and to the second position which is our ambition.”