Arsenal turned on the style against Fulham, recording their biggest win of the season.
Chelsea head Group L with a maximum six points with PAOK level on three points alongside BATE Borisov.
Unai Emery's side were under the cosh in the second half at the Emirates Stadium.
Ozil's agent Erkut Sogut, who Bierhoff had reportedly contacted before the visit, declined to comment on the reason for the rejection.
Unai Emery's side rode their luck in the first half at the Emirates Stadium as Everton wasted a host of chances to punish a sloppy opening from the Gunners.
Jerome Boateng was one of the few German players to speak up for Ozil after his retirement.
Olivier Giroud, who moved to Chelsea in January, believes the battle with Alvaro Morata is positive for the team.
Arsenal defeated Ukraine's Vorskla Poltava 4-2 in the Europa League, while in-form Chelsea registered a 1-0 win away to PAOK in Greece.
The likes of Arsenal, Chelsea, AC Milan and Sevilla will be seen in action in the Europa League group stage, which gets underway on Thursday.
Rafa Benitez's side quickly ran out of attacking ideas and intent.
KL Rahul and Umesh Yadav paid a visit to Arsenal's Emirates stadium to watch a Premier League match.
Shkodran Mustafi headed Arsenal ahead before Victor Camarasa equalised in first-half.
Liverpool will host Chelsea in the third round of the League Cup.
Unai Emery's side lost the first two games of the post-Arsene Wenger era against Manchester City and Chelsea.
Arsenal midfielder Mesut Ozil, 29, announced his shock retirement from international duty last month in the wake of Germany's World Cup debacle.
Chelsea's second successive win under new boss Maurizio Sarri lifted them to the top of the Premier League with a 100 percent record.
The Gunners were largely outclassed by the Premier League champions on Sunday.
Raheem Sterling opened the scoring with a cool finish early in the first half before Bernardo Silva lashed in City's second after the interval, leaving Guardiola to sing the champions' praises.