Dreesen said an agreement had been struck "in principle" with the Spanish club, with the 2010 World Cup winner due in Munich later on Thursday for a medical and to discuss terms. The addition of xabi in the squad could upset a few players who have been regulars in the line up.
The 32-year-old would become the fifth Spanish player on the Bavarians' books together with Pepe Reina, Juan Bernat, Thiago and Javi Martinez.
Shaqiri: Could leave Bayern
Bayern on Wednesday completed the signing of Mehdi Benatia from Roma for a fee of £20.7million and they were not expected to venture into the transfer market again this summer.
Alonso's arrival could see Xherdan Shaqiri seek a move away from the club.
The Swiss international winger is attracting interest in Italy, with Juventus and Inter Milan both keen on the former Basel midfielder.
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