Spanish international Alonso had been linked with a move to Juventus all summer, with his departure expected to pave the way for Liverpool to sign Aston Villa captain Gareth Barry as a replacement.
But Cobolli Gigli suggested Danish international Poulsen's arrival would result in Alonso remaining at Anfield.
"I am convinced that we have made a good choice by acquiring Christian Poulsen," he added.
"The signing is not a bet made by [Claudio] Ranieri but rather a tactical decision taken by Juventus, knowing that a powerful attack can only be supported by a strong midfield."
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