Amelia is playing second fiddle at Milan this season behind Christian Abbiati.
"I can confirm that Spartak are following him with interest," representative Carlo Pallavicino told Milan News.
"They have been monitoring his performances and they even sent some observers to watch him when Milan were in Dubai last week.
"Spartak wanted him four years ago and Amelia had already had his medical until [Livorno President Aldo] Spinelli changed his mind and the deal collapsed.
"However, over these years the admiration from their club officials for Marco has continued."