The Black Cats took a major stride towards safety on Saturday with a 2-0 win over Wigan which eased them into 14th place in the table while fellow strugglers Fulham, Bolton, Derby and Reading were all beaten.
It was Sunderland's fifth win in their last seven league games at the Stadium of Light, and took them within two points of their rivals as Kevin Keegan's men surrendered a 1-0 lead at Aston Villa to lose 4-1.
The Wearsiders have now taken 12 points from the last 27 on offer, nine more than the Magpies, whose relative comfort at the turn of the year has all but evaporated.
However, while the red-and-white faithful contemplate the prospect of overhauling Newcastle - they head for Portsmouth in a fortnight's time as Keegan's side entertain Manchester United - Roy Keane and his players remain solely focused on the three points at stake at Fratton Park.
Collins said: "Deep down, that's what the fans would like, but our first aim is to keep our status in the Premier League.
"If we can get above Newcastle, that would be another plus for us.
"We are two points behind them, but our main aim is to stay out of that bottom three."
Sunderland's home form - they have taken 16 points from a possible 21 since the start of December - has given them a genuine chance of remaining in the top flight.
But despite a return of just two points from a possible 39 on the road, Keane has never doubted his side's ability to make it to the finishing line, and nor has he allowed his players to .
Collins said: "There has always been a confidence among the lads - the Gaffer wouldn't let it go any other way.
"He is a confident talker and he gets wired into the boys before the game.
"We know deep down within ourselves if we go out there on a Saturday and put on a good performance, we have got enough to come away with at least a point.
"Thankfully, we have managed to do that against the teams who have come up here in the last few weeks."