The Frenchman scored a goal of jaw-dropping quality at St James' Park on Monday to set the Magpies on their way to a hard-fought 2-0 victory over Bolton, their fifth successive win in the Premier League.
It left them level on points with fourth-placed Tottenham, who lost 2-1 at home to promoted Norwich, with five games of a wholly unexpected campaign to go.
Asked about the possibility of a top four finish, Pardew replied: "I have never actually ruled it out.
"You guys kept saying to me, 'Are you going to make the Champions League?', and I said we were just looking to win the next game.
"But look, it's not gone unnoticed. This week could be important for us because if the [FA Cup] semi-final results go our way, we could be in Europe, I think, by next weekend.
"If that works in our favour, then really, really there is nothing left to go for but the Champions League.
"That's important to us, the semi-finals, we will be looking at them because we are up against Chelsea for that Europa League place if the results go against us, and that's still very, very tough on us.
"To have this points total and not make Europe would be tough to take, so we have got to keep our eye on the ball, and we ain't giving up on anything - apart from winning it."
The Champions League may prove to be a dream for Newcastle this season, but the quality of the goal which sent them on their way to their latest victory would certainly not have been out of place on that stage.
Bolton were actually enjoying the better of a drab encounter when, with 73 minutes gone, Ben Arfa took it upon himself to embark upon an outrageous run from deep inside his own half after turning away from defender Sam Ricketts.
The sense of anticipation grew as he sprinted past Mark Davies and then between central defenders David Wheater and Tim Ream before sliding a shot beyond keeper Adam Bogdan.
Pardew said: "I am a lover of football. You don't see too many goals like that. I have been lucky enough to see two of them this year, both from the same player. It was a truly special goal.
"It's going to get Premier League coverage and he is going to get all the plaudits, and so he should for a goal of that quality.
"As I have said in here before, he should definitely have a chance for the French squad.
"There are not many players who can do that, and the French manager needs to understand that not only did he get that goal today, he had a hand in the second and his work-rate was phenomenal."
Ben Arfa's strike came as a massive blow to Bolton, who had earlier passed up two glorious opportunities to take the lead in a tight encounter.
Keeper Tim Krul produced vital saves to deny first Chris Eagles and then Mark Davies after the break to set the stage for the Frenchman's heroics.
Papiss Cisse gave the Magpies breathing space seven minutes from time when he turned substitute Shola Ameobi's cross home from close range to claim his 10th goal in nine appearances.
Defeat left Wanderers poised precariously just above the drop zone, but the performance bolstered manager Owen Coyle's belief that they can stay up.
He said: "We accept Ben Arfa's finish was quality; for our part, there was a lot to be pleased about.
"The disappointment is we are left with no points, but what I do know is if we offer that level of performance for the total duration of a match, then we will pick up enough points to stay in the Barclays Premier League, and that's what we have to do."
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