Saturday's 1-1 draw at struggling Blackpool took Newcastle onto 41 points, seven clear of the drop zone with four games remaining.
That total should ensure the Magpies remain in the top-flight for a second season but Ameobi reveals the squad are now focused on staying in the top-ten, and above their neighbours.
The Black Cats have spent the majority of the season above the Tynesiders, despite October's 5-1 thrashing at St James' Park, but their recent slump saw them slip into the bottom half of the table.
However, Saturday's win against Wigan catapulted Steve Bruce's men back into the top half, level on points with Alan Pardew's men but Ameobi insists his team-mates are eager to finish as top dogs in the North-East.
"I think so yes, quietly," the 29-year-old said.
"You want to finish as the top team in the region. It didn't look very likely until a few weeks ago but we've dug in and done well as of late while they've had a poor run. They got a great victory against Wigan.
"It's something we're focusing on but we'll take it game by game and hopefully finish on top.
"We're taking it game by game. We said after the great result on Tuesday we didn't want to fall back with a disappointing loss in the next game.
"We knew the importance because it's easy for us to raise ourselves against the big teams and not really do ourselves justice against the likes of Blackpool.
"We showed the character we have. We didn't really play our best football but we dug in and that's a great sign of the future. We know we have to work hard every day we play, and we did."
Next up for the Magpies is a difficult trip to Anfield to face an in-form Liverpool side, who have lost just one of their last six games.
It will be the first time the sides have met since Andy Carroll's shock transfer to Merseyside in January. The £35million striker missed Liverpool's 5-0 win over Birmingham through injury but Ameobi says the Magpies will expect a tough test regardless of whether their former team-mate plays or not.
"With Carroll or without Carroll I'm looking forward to it," Ameobi said.
"It's a game that historically hasn't been great for us but I think we're trying to turn tides here on Tyneside.
"Hopefully we can get another massive result. We beat them at our place earlier in the season so it's not impossible.
"It will be a tough game with or without Andy playing. We just have to be focused and hopefully we can come through that one."