The exchange came at the end of Arteta's post-match media duties following Arsenal's 4-1 pre-season win over Girona on Saturday, with the Real Madrid winger having dominated speculation around the club throughout the build-up.
Vinicius, 26, is viewed as a potential option to strengthen the left-hand side of Arsenal's attack, an area regarded as relatively weak within an otherwise title-winning squad, and scored 22 goals with 14 assists in 53 appearances for Real Madrid last season despite a difficult campaign for the Spanish club. Talks over a new contract at the Bernabeu have reportedly stalled, a situation Arsenal are said to see as a genuine opportunity.
Arteta had already been asked earlier in the press conference whether fans could expect further signings before the season starts, and gave a fuller answer without naming Vinicius directly: "Well, we are really active, trying to improve and evolve the team.
"That's clear. We expect to have movements in the next few weeks, obviously, because we want to get better like anybody else. And you can just see it. The transfer market and our opponents, what we are doing, we won't sit still. And we are very ambitious in what we want to do."
It was the final question of the press conference, though, that produced the more telling reaction. Asked directly when Vinicius would be joining, Arteta simply smirked, replied "Thank you so much," and left, declining to engage with the question at all.
The brief, pointed exchange has only added to the sense that talks over a move remain live and sensitive enough that Arteta was unwilling to say anything that might complicate them in public.
Left wing has been an area of focus for Arsenal all summer, with Gabriel Martinelli's long-term future uncertain and Leandro Trossard having already departed for Besiktas. A move for Vinicius would represent one of the most eye-catching signings of the entire Premier League window, though Real Madrid have shown no public sign of being ready to let their winger leave, and Arteta's refusal to be drawn on the subject suggests any deal, if it happens, is unlikely to be confirmed through a slip in a press conference.