Alonso had a medical this morning and the Reds are just waiting for the results before completing the deal.
Manager Rafael Benitez said: "We are just waiting for his medical results now. We should get them later today and he can then sign his contract.
"Signing Xabi and also Luis Garcia will make us a better team and a stronger team."
Alonso will not be eligible to play against Man City tomorrow so will probably make his debut against AZ Graz on Tuesday.
