Neither player has managed to make a big impact this season, with the Mariners sitting ninth on the A-League ladder after last weekend’s 2-1 home loss to Brisbane Roar.
It’s understood the club will not stand in the way of either if deals can be done, with Appiah-Kubi to attract a small fee, and Rose to have his contract terminated if an agreement with City is reached.
Appiah-Kubi, 25, has scored two goals in 38 appearances since rejoining the club two seasons ago, after stints with Western Sydney Wanderers and Wellington Phoenix.
The Mariners have netted 18 goals this season - the joint lowest in the competition - with Appiah-Kubi seemingly not the solution to their woes.
Negotiations are on-going with an unnamed Korean club, with their transfer window closing in March.
Rose, 20, has made just three starts this season - and seven appearances off the bench - as Mariners coach Paul Okon has instead opted for Dutchmen Wout Brama and Tom Hiariej in the midfield engine room.
Club insiders claim his attitude has been at times questionable, one of the reasons for his fall down the pecking order.
Just two seasons ago, Rose was hailed as one of the club’s bright young lights after winning the Mariners Medal, but his career has stalled since.
Back then there was interest from Sydney FC and Melbourne City, who are now in for a second bite, despite having the likes of Osama Malik and Luke Brattan in his position.
Rose has made 63 appearances for the club after being snapped up from the AIS by former coach Graham Arnold four years ago.