Defoe moved to the Stadium of Light in the January transfer window and got off the mark for his new club in a 2-0 victory over Burnley last weekend.
The former Tottenham striker once again showed why head coach Poyet was so desperate to land him from MLS club Toronto when he opened the scoring with a clinical 18-yard finish in Saturday's 1-1 draw at Swansea City.
And Poyet believes that Defoe still has the quality to add to his 55 England caps, the last of which came against Chile in November 2013.
"When you pick a team you pick strikers who are on form," said the Sunderland boss ahead of Tuesday's encounter at the Stadium of Light.
"You see [Tottenham's] Harry Kane, he's an obvious choice.
"But Jermain has a chance if Wayne Rooney plays in midfield [as he has been doing recently for Manchester United].
"Jermain scored again. It's up to [England manager] Roy Hodgson, I respect the manager of the national team.
"The only thing the players can do is perform and show they want to play. That's good for the country when a player wants to play. Then the manager decides."
Poyet confirmed that forward Connor Wickham (calf) is likely to miss a third consecutive match, while Emanuele Giaccherini (knock) - who was set to be in the squad against Swansea but pulled out before the warm up - remains sidelined.
However, the Uruguayan could welcome Jack Rodwell (knock) back into his squad.
QPR, who are 19th, head north having started the post-Harry Redknapp era with a demoralising 1-0 defeat to Southampton - Sadio Mane's injury-time goal condemning them to a fifth straight defeat in all competitions.
A permanent successor to Redknapp, who resigned his post on Tuesday, has yet to be appointed, meaning Chris Ramsey and Kevin Bond remain in caretaker charge.
Ramsey - who stated after the Southampton match that he may not be at the helm by the time QPR travel to Hull City at the weekend - has outlined the importance of claiming points over the next seven days.
"We've got a game on Tuesday to try and make things good," he said.
"Our next two games are massive. We can't afford to not be on our mettle."
QPR are still to pick up a single point on their Premier League travels this season, but they did beat Sunderland 1-0 in August's reverse fixture.
Charlie Austin, the scorer of the only goal in that game, will miss out on this occasion with a foot injury he picked up against Southampton, although scans have revealed the issue is not as serious as first feared.
Centre-back Richard Dunne is sidelined after picking up a knee injury in the same game.
