Former club legend Lothar Mattheus has questioned the transfer policy in Bavaria, suggesting there was better value in retaining the Germany international
Germany international Kroos departed for Real Madrid in the summer after protracted discussions over a new and improved contract with the reigning Bundesliga champions, with reports suggesting the club were unwilling to meet his demands for a wage increase.
Alonso moved in the opposite direction last week and Matthaus believes €10 million transfer fee and the salary being paid to the 32-year-old would have been better invested by keeping Kroos at the club.
Kroos joined Real Madrid for a fee believed to be around €25 million.
"“I was surprised," Matthaus, who won seven league titles in two spells at Bayern as a player, told SID.
"They lost a German world champion to Real Madrid. For the salary that Alonso is now being paid, they probably could have kept Kroos.
"[Sami] Khedira interested those at Bayern Munich but not Guardiola," he added, suggesting that the club preferred to sign another Germany international.
"Bayern seem to have gone a bit astray, but that’s their right."
Alonso made his Bayern debut on Saturday they Guardiola’s side stumbled to a 1-1 draw with Shalke after having openied their Bundesliga campaign with back-to-back victories