Carlo Ancelotti's men have not tasted defeat since the end of October and went top of La Liga last weekend thanks to Atletico Madrid and Barcelona's respective losses to Osasuna and Real Sociedad.
And while the former Liverpool midfielder acknowledges that there is plent of work still to be done, he believes that he and his team-mates are capable of winning trophies.
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"It’s very difficult to speculate on what will happen between now and the end of the season," he said at a press conference.
"We’re well-positioned and the overall mood is positive but as I say, that can easily change. We have a good squad, some players have come in and others have left.
"We’re confident, whilst knowing that we still have a lot of games to get through."
Alonso spent a spell on the sidelines with a foot problem earlier in the season but says that he is now back to full fitness.
"I’m over my injury now, it’s in the past. The team is hitting form, we're ready for this decisive stage of the season - March, April, May.
"We’ll take it step by step, starting with tomorrow’s game which is a crucial game for us."