Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
And Rams chief executive and president Sam Rush believes the subsequent appointment of Steve McClaren as head coach could even increase the chances of the Manchester United centre-half coming to Pride Park.
Clough had agreed a deal to sign Keane, who had a successful loan spell with Leicester last season, but he was sacked on Saturday following the Sky Bet Championship defeat to east midlands rivals Nottingham Forest.
McClaren was unveiled as his successor on Monday, when Rush refused to deny the deal was dead.
"I think with his relationship with Manchester United, Michael Keane has more opportunity of coming to this club with Steve McClaren as head coach," said Rush.
"That is one area we are generally looking to move forward with in the current set-up, to have those connections. I think that is a key area where we could find our competitive advantage.
"If we can forge relationships with top clubs that can certainly help us.
"I think if top clubs can see that their young players will continue to be coached to a really high level at Derby then they will be very happy to place them with us."