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.
Victor Orta knows former Leeds United favourite Adam Clayton from his time at Middlesbrough.
Pep Clotet is reportedly under consideration for the Leeds United job.
Manchester United forward Wayne Rooney is said to be keen to return to Everton.
Manchester United have been linked with Tottenham Hotspur’s Eric Dier and AS Monaco midfielder Tiemoue Bakayoko.
Lambert is widely expected to leave Wolverhampton Wanderers this summer, which could be good news for Sunderland.
The former Watford boss was allegedly offered the role at Leeds United.
Tottenham are reportedly looking to bring a host of new signings to the club this summer.
Tottenham could grab a bargain as Schalke put Max Meyer up for sale.
Rangers boss Pedro Caixinha came up against the reported Ibrox target while managing in Mexico.
Ross Barkley is out of contract at Everton next summer, and is attracting attention from Tottenham Hotspur.