"He's too old!"
"He's not worth that much a week!"
"Oh no, not another Chelsea reject!?"
These objections are entirely valid - the winger is nearly 32 and will demand a hefty wage - but Willian has attributes this Arsenal squad lacks. As Mikel Arteta looks to build a squad capable of league success, the Brazilian may have an important role to play.
At the beginning of last season, Arsenal sported the youngest squad in the Premier League with an average age of 25.1. They've made it known they wish to target younger players who can reach their potential at the club, instead of heavily investing in players already in their prime.
It's the right approach, given the financial restrictions in place at the Emirates, and points to some welcome long term planning. This new policy is a move away from what it has been in recent years, when the transfer strategy had very much been focused on the here and now.
The signings of Sokratis, Henrikh Mkhitaryan and Stephan Lichtsteiner - made with the hope they could help the club return the club to the Champions League - weren't exactly roaring successes.
However, it is essential that this current crop of young players is balanced with some experienced heads. If Sokratis and Mesut Ozil were to leave this summer, Pierre-Emerick Aubameyang and Luiz would be the only players in the squad over the age of 30.
Willian is a serial winner - he has lifted silverware during his time in England and Ukraine with a regularity most players can only dream of. He knows how to win. For the majority of this young Arsenal team, their recent FA Cup triumph was just their first taste of success, but Willian's experience and mentality could help them become ravenous for it.
You need look no further than Luiz to see Arteta recognises the importance of experienced figures in the squad. When many expected the Brazilian to leave at the end of the season following a string of dismal performances, Arteta insisted he stayed. It seems the reason isn't just the centre back's performances on the pitch.
The Brazilian's influence and experience in the dressing room has been highlighted by many of Arsenal's youngsters as instrumental to their growth and confidence this season. Bukayo Saka notably singled out Luiz for praise upon signing his contract extension recently.
Were Willian to join, he could be equally instrumental to the development of these young talents. Gabriel Martinelli, Saka and Reiss Nelson, being wingers themselves, stand to benefit from Willian's tutelage.
A lot was expected of Arsenal's youngsters this season, and at times it was too much. But signing Willian would help alleviate the burden on these players, allowing rotation and rest when necessary. His arrival could also offer the chance for one of those young forwards to gain some valuable minutes out on loan, with Nelson the obvious candidate.
But make no mistake, Willian wouldn't be signing just to be an old head. Regardless of age, he is still an excellent player and would play an important and regular role in the Arsenal team next season as they look to push up the table into Champions League places.
With 11 goals and ten assists this season, Willian's contributions rank him only behind Aubameyang in the Arsenal squad. Nicolas Pepe has finished the season strongly, but still managed two fewer goal contributions than Willian this season.
Arteta has managed to fix the seemingly impossible task of improving Arsenal's defence but, aside from Aubameyang, there has been a dearth of goals in this squad. Willian has a proven track record and his contributions next season will be key if Arsenal are too continue to progress.
The Brazilian would also provide Arsenal with a different option in attack. While Aubameyang and Pepe have featured regularly on the wings, both are more comfortable playing as inside forwards. When Arteta has tasked Pepe with playing as a more traditional winger, he has struggled. Willian would provide a proven solution to this issue.
His ability to beat his man and get to the byline before cutting the ball back across goal is an area Arsenal have lacked in this season- the type of chance Alexandre Lacazette feeds on. Willian's arrival therefore may be instrumental in getting the Frenchman back to his best next season.
Willian offers stability on the pitch and off it. This is a smart deal in a time of financial constraint. Raul Sanllehi said recently Arsenal need to "outsmart the market," and this move would back that statement up.