The likes of Massimiliano Allegri, Eddie Howe and former player Patrick Vieira have also been placed in the frame. In an age where 'knowing the club' is seemingly among the most vital requirements, Vieira, Mikel Arteta and indeed Ljungberg all have a chance, while Allegri is among the biggest names on the market and Howe has impressed everyone at Bournemouth.
Arsenal are in crisis territory for a club viewed as one of the iconic institutions of English football and where they turn next could be huge in determining both their short- and long-term future.
They've slumped to tenth in the Premier League standings and will finish a decade of failure on a low note. Unless the club rethink their vision, it could be a few more decades before they return to the summit again.
They need a manager with a strong identity, someone who can wake up a sleeping giant. Arsenal should look no further than Marcelo Gallardo.
What we saw during that 2018 run, and indeed throughout his time back in Buenos Aires, was Gallardo's ability to adapt his tactics.
River opted to go for a 3-4-1-2 formation in the away leg of the final against rivals Boca Juniors, which finished in a 2-2 draw. They would then switch back to something that resembled more of a 4-2-2 in the 'home' leg which was enough to secure an aggregate victory.
So not only has he rebuilt this squad to maintain their elite status, he's created an environment that allows him and his players to modify and change and adapt.
A rebuild can often be costly, but Gallardo has proven to hold a sensible approach to the transfer market.
The 2015 window did bring a host of new players but not with the bill that usually come with 11 new additions. Less than £9m was spent in a season that then yielded two trophies, a final appearance and a spot in the final four of the Copa Sudamericana.
This season saw one new addition - Chilean defender Paulo Diaz. River went onto make the final of the 2019 Copa Libertadores.
There's not only the signings, but also the ability to use River's academy which would provide great appeal to a club like Arsenal and the host of talented youngsters they possess.
During his spell in charge, Gallardo has given 31 youth players their debut with the senior side.