The Reds can overtake United to go top of the Premier League if they beat Fulham next Saturday.
And Spanish star Alonso believes they can pile on the pressure after Alex Ferguson's men lost their last two matches.
He said: "It's going to be difficult because we can't afford to drop many points and we know that United have a very good team.
"They are the main favourites, of course, but we are going to be doing our best to be challenging until the final weeks of the season.
"I think the pressure is on United. They are the champions.
"They are in the best position and they have that advantage.
"We have to do our job and try to make things difficult for them.
"At the moment the team is playing and defending well as a team. The partnership between Steven Gerrard and Fernando Torres is working well for us.
"Of course Torres is really important for us. When he's fit he's a threat for all the defenders and that's a boost for us."