The West African duo have been key performers for the Magpies in recent years, but with the club in the process of an overhaul they are keen on moving onto greener pastures. United have also suffered seven straight defeats in the Premier League.
Tiote, 28, Cisse, 29, along with Dutch goalkeeper Tim Krul and French midfielder Moussa Sissoko, are angling for moves away from St James Park in the European summer, according to the Sun.
A further 10 players are also set to see their contracts expire or move away from the club, which has yet to name a permanent manager following the departure of Alan Pardew earlier this season.