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.
Sullivan has just completed a loan spell at AFC Wimbledon and Mambo was most recently on loan with Shrewsbury.
Addicks manager Chris Powell said: "Those lads will be looking to play elsewhere. We are trying to be fair to them.
"John has been a terrific character, trainer and goalkeeper for us, but he needs to play regularly.
"He has just had a good taste of that and hopefully, whether it is at Wimbledon or elsewhere, he needs to get going.
"It is the same with Yado. He has had a taste of League Two and League One this year.
"The reports were good but I said to him once you get that week in, week out feeling of preparing and playing he would find it hard to play here."