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.
Millwall say they have yet to choose a new manager amid speculation former Liverpool defender Markus Babbel is set to get the job.
Babbel has emerged as a surprise contender to succeed Kenny Jackett, who quit at the end of the season after almost six years in charge at The Den.
The Lions are understood to be looking to Europe for their next boss and ex-Germany international Babbel, 40, would fit the bill having previously guided Hertha Berlin to promotion as well as managing Stuttgart and Hoffenheim.
But Millwall chief executive Andy Ambler has played down talk of an imminent appointment.
"It is true we now have shortlist of some half a dozen candidates and the interviewing process will begin at the end of this week," Ambler told the club website.
"No decision is likely to be made within the next 10 days or so, and indeed I would anticipate that we would speak to some candidates more than once before we are ready to make an appointment.
"The reality is that the process is just getting under way and at this stage there is no preferred candidate."