The 23-year-old, who sees his current deal expire at the end of June, played 25 Premier League games last season.
Whilst Ameobi has been offered a new deal, three other players who are also out of contract will leave the club when their contracts expire on30 June.
Jak Alnwick, Adam Campbell and Remie Streete will all be seeking pastures new next season, whilst Facundo Ferreyra returns to Shakhtar Donetsk after completing his one year loan deal on Tyneside.