The Italian side were keen to strengthen their squad and identified Baggies midfielder Mulumbu as somebody who could come in and make an impact.
There were a number of other players on their wish-list but none arrived and, despite making a solid start to the season, Cognigni still has regrets.
"In the summer we considered Axel Witsel, Mulumbu and Arouca. For many reasons we could not take them," he told Corriere Fiorentina.
While Mulumbu stayed with West Brom, Belgium international Witsel opted for a move to Benfica from Standard Liege and Brazilian midfielder Arouca remained on the books of Santos.
Cognigni added: "We also made many attempts for (Sampdoria captain Angelo) Palombo, until the penultimate day of the market."
Cognigni has also spoken of his disappointment at the ongoing saga regarding Riccardo Montolivo's contract.
The 26-year-old's current deal expires at the end of the season and no agreement has been reached over an extension.
While Fiorentina had hoped to keep the player, he appears determined to keep his options open and has been linked with a move to Arsenal.
"The negotiations for the renewal of Montolivo left me a deep bitterness," said Cognigni.
"They (Montolivo and his agents) pretended to be willing to reach an agreement, but the will was not there. In fact, it was the opposite.
"He would not even agree to go away, refusing an offer of Roma, who offered us €10million plus bonuses.
"In his last meeting with (Fiorentina owner) Andrea Della Valle, Riccardo said 'I want to leave on a free transfer, so I'm sure there will be more chance to go to a major club'."