This summer, it has been made clear that the defence needs to be strengthened.
With Carles Puyol retiring and Javier Mascherano likely to play in a midfield position, Barcelona were left with just two centre-backs, Gerard Pique and Marc Bartra.
The former of those two has been in dire form, while the latter is young at 23 and has yet to undertake a full season as a first-choice player.
So they spent €20 million on Jeremy Mathieu, who now appears first choice for the left-sided centre-back role.
Barcelona still want to add another defender, but if it is Vermaelen, it is hard to see the point.
The Belgian has been out of favour at Arsenal, with Arsene Wenger opting for the Per Mertesacker and Laurent Koscielny partnership.
Vermaelen has been with Arsenal for five years, so Wenger would not have made such a decision lightly.
The fact of the matter is that the Frenchman and the German formed an effective partnership. When Vermaelen played, his game was flawed.
Wenger told the Daily Star, h/t Sport, "For me, Thomas is an important player but I could not give the games he wanted last season, so we'll see what happens."
There is a place for another defender at Barcelona, but only if it is a world-class one who can step straight into the side.
If Vermaelen was brought to the Camp Nou, he would not walk into the team.
So unless Barcelona plan to sign a top-class player, they may as well move forward with the three they have and use Mascherano as a fourth choice.
Furthermore, Vermaelen is left-footed, so he would be vying for the same position as Mathieu.
While some have concerns about Mathieu's suitability for a team challenging for La Liga, the Copa del Rey and the Champions League, he is on the same level as, or perhaps even better than, Vermaelen.
However, there is a shortage of truly great central defenders on the transfer market at the moment.
Paris Saint-Germain paid a premium when they splashed €50m on David Luiz from Chelsea.
In turn, Barcelona are trying to procure Marquinhos from the French side, but that is proving virtually impossible.
Per Sport's Joaquim Piera, Nasser Al-Khelaifi, PSG's president, considers the matter closed; Marquinhos is staying in Paris.
Barcelona aren't left with much choice. Roma's Mehdi Benatia and Borussia Dortmund's Mats Hummels are two of the better players out there who would appreciate moving to bigger sides.
If they have €40m to spend on Marquinhos, they would be advised to spend that on one of those two players.
Paying €12m for Vermaelen would solve a problem on paper, but, in reality, it would leave Barcelona just as fragile at the back.
They would be better off spending more or not buying anyone at all.