The Liverpool forward was in impressive form in the 4-3 victory at the Emirates.
Everton and Tottenham drew 1-1 on the opening day of the new Premier League season.
The Eagles are interested in the West Ham striker if a move for the Liverpool forward fails.
The Reds beat Arsenal 4-3 at the Emirates on Sunday.
Leeds United and Birmingham City faced each other in the Championship on Saturday.
Rangers are being linked with a move for Joe Garner.
With Lazar Markovic, Iago Aspas and Tiago Ilori all flopping at Anfield, Jonathan Woodgate has his work cut out if he takes a scouting role at Anfield.
Paul Trollope's Cardiff City lost 2-0 to Jimmy Floyd Hasselbaink's Queens Park Rangers at the Cardiff City Stadium.
Alexandre Lacazette has interested Arsenal for the entire window but is now set to remain in Ligue 1 after admitting he has unfinished business.
Liverpool boss Jurgen Klopp has praised forward Sadio Mane.
Gabriel Batistuta believes former Tottenham Hotspur defender is among the best in the world.
Armstrong has endured a swift fall from grace at Celtic.
Newcastle United are said to have £30 million to spend on new players in the January transfer window.
Brighton winger Jamie Murphy was linked with Celtic and Rangers in August - and the Old Firm rivals may be in an excellent position to try again in January.
Former Liverpool star says club should have sold Daniel Sturridge two years ago.
Liverpool failed to win in the Premier League on Wednesday.
Newcastle United are reportedly lining up January signings.
Everton striker Wayne Rooney has been in wonderful form since Sam Allardyce took charge.
Leeds United are back in Championship action this weekend.
Everton won against Newcastle United to continue their fine start under Sam Allardyce.