The three internationals will head a list of squad players that sporting director Lee Congerton is eager to move on.
Gus Poyet does not see the trio as vital to his plans, while allowing players to leave could allow him to rebuild his current squad.
The trio cost a combined fee of nearly 20 million pounds when they arrived in the summer of 2013 under then coach Paolo Di Canio, but none have been able to make a significant impact on the first team.
Giaccherini, who costs close to £9m, has started just three leagues games in 2014, while winger Mavrias has been named in the starting lineup just once in the Premier League since he arrived from Panathinaikos.
Altidore has dropped down the pecking order - he is without a league start since March - and admitted only last week that he might have to consider a move away from the Stadium of Light.
Sources have confirmed to Goal that Sunderland hope to find buyers for Altidore, Giaccherini and Mavrias, as well as fringe players Cabral and Danny Graham - who have been told they are surplus to requirements.
"There are a number of players the club now deem surplus to first-team requirements and they will be working hard on getting them out as soon as possible, which will mean January," the source said.
The future of Connor Wickham remains up in the air, but Sunderland still hopes to persuade the young striker to sign a new long-term contract at the Stadium of Light, with his current deal set to expire in the summer.