United are 15 points behind leaders Liverpool and four points off the Champions League spots after 13 matches.
Arteta was asked at his pre-match press conference on Tuesday whether United could be in the title mix despite their poor start to the season under the sacked Erik ten Hag.
"It's still very early in the season," said the Spaniard, whose team are second in the table, six points clear of United.
"Any team that has the capacity to put five or six wins in a row is going to be up there because it's so tough and you see every week how all the teams are struggling to maintain winning, winning and winning. So I think anything is possible."
And Arteta said champions Manchester City were still a danger despite their recent slump -- Pep Guardiola's men have lost their past four league matches to fall 11 points behind Liverpool.
"Again, if there is a team with the capacity to turn it around and start to win, win, win and win –- don't rule them out because you know how much quality they have," he said.
Arsenal have a good recent home record against United, who have won two and drawn one of their first three games in all competitions under Amorim.
Arteta said he could already see the influence of the former Sporting Lisbon boss, just weeks after he replaced Ten Hag.
"You can see his fingerprints in what he wants to do straight away," he said. "I think he's been very clear, he's been very successful with Sporting.
"He brings energy to a new club and to the players new ideas and that's always something positive but we have to focus on what we have to do."
Arsenal have also been drawn against holders United in the third round of the FA Cup, which takes place early next month.
"We play at home, it's going to be a big match again and it's a little bit of the story of the last few seasons that in the third or fourth round we are playing big opponents," he said.
"But we want to do what we have done historically at this club and in the end, you have to beat the big teams to win it. It is what it is. We are excited."
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