Manager Alan Pardew revealed after his side's 4-2 Barclays Premier League victory over Southampton on Sunday that the two clubs will hold talks over the 20-year-old.
Pardew said: "We are going to talk to Middlesbrough. I would like to help Middlesbrough out if they want him, and hopefully we can conclude that."
Ameobi, the younger brother of striker Shola, has made 14 senior appearances, eight of them as a substitute, for the Magpies to date this season.
Newcastle last week