Arteta’s young team produced a second-half fightback to beat West Ham and move seven points clear at the top of the Premier League, which was resuming after the World Cup.
Wenger, who was the last Arsenal manager to win the title, made his first return since stepping down in 2018.
“His presence is something that has to be very, very attached to this football club so thanks [to him] for doing that because it means a lot for everybody at the club,” said Arteta.
“Hopefully he is willing to spend more time with us and be around us because he is such an influence.”
Relive all the action as the Premier League returned on Boxing Day
West Ham took the lead against the run of play when Jarrod Bowen was judged to have been clipped in the box by William Saliba, allowing Said Benrahma to smash a confident penalty down the middle.
There was a mood of frustration among the home fans until Bukayo Saka converted from close range after collecting Martin Odegaard’s mis-hit shot.
The equaliser gave added impetus to the Gunners and another home goal looked increasingly likely.
Five minutes later, it duly arrived. Gabriel Martinelli put the hosts ahead, catching out West Ham’s former Gunners keeper Lukasz Fabianski by tucking inside the near post from a tight angle when he seemed more likely to cross.
The points were sealed when Eddie Nketiah – starting in place of the injured Gabriel Jesus – spun sharply in the box before firing into the opposite bottom corner.
Arsenal extended their lead at the top over Newcastle, who moved second by beating Leicester earlier on Monday.
Reigning champions Manchester City – who go to Leeds United on Wednesday – are now eight points behind the Gunners.
West Ham are 16th and just a point above the relegation zone after their fourth league defeat in a row.
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Arsenal show progression on Arteta anniversary
Arsenal fans are starting to believe Arteta’s side can genuinely maintain their push for the club’s first title since Wenger’s Invincibles in 2004.
And as Wenger watched and heard his name lovingly sang by the home crowd, Arteta’s young team added further encouragement to those dreaming of a long-awaited triumph.
“It is a really special day because Boxing Day is a beautiful day to play football and I thought the performance was at the level today that we deserve,” said Arteta.
“Hopefully he [Wenger] will like it.”
The match came on the third anniversary of Arteta’s first game as Arsenal manager, and significant progress has been made since then.
When the former Gunners midfielder took over, they were closer to the relegation zone than the top four.
Their current position – and mood around the club – is a measure of how they have come.
The Spaniard has built a new team in the past three years which bears little resemblance – in style and substance – to the one picked for his first game at Bournemouth in 2019.
Arteta will not be getting carried after this win over West Ham, especially with several significant fixtures – not least against Manchester City on 15 February – on the horizon.
But the Gunners sent a message with a clinical second-half performance and the omens are also in their favour.
The team who topped the Premier League table on Christmas Day have gone on to be champions in 10 of the past 13 seasons.
Nketiah takes chance as West Ham struggle in front of goal
One of the key questions as the Premier League returned was how the Gunners would cope without key striker Jesus.
The Brazil international had knee surgery after being injured in Qatar and is expected to be out until late February, fuelling talk the Gunners might need to sign some cover.
But against West Ham, a first Premier League start of the season was handed to Nketiah – and the 23-year-old delivered.
After stretching the Hammers defence and creating space with his sharp movement, he capped an impressive all-round performance with a fierce finish and staked his claim to be Jesus’ replacement.
“Gabby will be a big miss but we all believe in Eddie,” Saka told Amazon Prime. “That’s all he needs, us to keep supporting him and we will keep encouraging him.
“Everyone in the team is chipping in [with goals] and everyone will be important.”
In contrast to the leaders, West Ham are struggling in front of goal.
They have been better than their league position suggests, according to their expected goals statistics, with converting chances being their main problem.
Few opportunities came against Arsenal, although the game might have panned out differently had Michail Antonio not been denied by Aaron Ramsdale shortly after the restart at 1-0.
Hammers manager David Moyes said before the match he has not been feeling pressure because of results, instead urging for perspective and togetherness across the club.
But a fourth straight league defeat leaves West Ham as one of the cluster of teams packed tightly together in the bottom half.
“I don’t think we’re in a relegation fight. Every team has a blip when it isn’t plain sailing and results don’t go your way,” said midfielder Declan Rice.
“It’s down to me as captain to keep everyone going and pushing. We still believe we are a top team. But we need to start showing that. It’s down to us.”