Milan CEO Adriano Galliani said the club tried to sign Axel Witsel but they were unable to complete a transfer before the Serie A transfer window closed on Monday.
Sinisa Mihajlovic and Co. were determined to bolster their midfield, with Belgium international Witsel at the top of the list of potential recruits.
However, Witsel remained in Russia when the deadline passed, despite months of negotiations.
"We tried to the end for Witsel, but we knew it would finish this way," Galliani told reporters.
While Milan failed to add to the signings of Carlos Bacca, Alessio Romagnoli, Luiz Adriano and Mario Balotelli, Alessandro Matri and Hachim Mastour were both loaned out to Lazio and Malaga respectively.
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