Gunners manager Mikel Arteta believes Brobbey can provide an alternative to the injury-prone Gabriel Jesus in attack.
A number of Italian clubs are also interested in signing the former RB Leipzig player.
However, it is thought that the midfielder is aiming for a move to the Premier League.
Brobbey, who scored 21 goals last season, is a member of the Netherlands’ Euros squad.
So he’s focused on Wednesday’s semi-final against England, knowing he may play in the country’s top tier next season.
However, Brobbey has already expressed interest in such a move.
He’s even singled out both of the Premier League’s leading clubs.
When purportedly asked which team he would support, he once replied, “Manchester United.”
More recently, he contributed to the suspicion by casting a wider net.
The twice-capped ace freely revealed the teams he most envies in terms of a potential transfer.
Brobbey told NOS Jeugdjournaal: “I think Arsenal is a very wonderful club. If you glance at the stadium. A really great club.
“However, that also applies to Manchester United, Barcelona, and Real Madrid. I’ve got a contract till 2027. At the time, I am only with Ajax.”
The Red Devils have been linked even more firmly with Brobbey’s international teammate Joshua Kirkzee, whom Bologna is fighting a losing struggle to retain.
And, despite reports that Slovenian hero Benjamin Sesko is set to extend his stay at Leipzig, he is still linked with both United and Arsenal.