Messi is eager for the Blaugrana not to stand pat defensively, even though Yerry Mina has already been signed, per the reports.
The Colombia international has made a solid start to life in Barcelona, with the defender impressing those within the dressing room, according to Marca's Ramiro Aldunate and Panos Kostopoulos. Even so, the same report also noted how 23-year-old Mina is yet to start.
Alaba fits the bill as a player who could bolster Barca's back line at more than one position. He can play at left-back and even spent time as a central defender on the watch of former Bayern manager Pep Guardiola.
Today's Barca squad can count on Samuel Umtiti at the heart of defence. The 24-year-old often plays as the left of the two centre-backs in manager Ernesto Valverde's starting XI.
Given Umtiti's position and strong form, Alaba would be a good fit for the Blaugrana at left-back. Spain international Jordi Alba still starts regularly, although Lucas Digne has filled in because of injury.
Alba is now 28 but would face serious competition from the younger Alaba. It's also possible the Austrian, who can even operate in midfield, would move further forward, where vital holding player Sergio Busquets is now 29.
Los Blancos' interest in Alaba is longstanding, with the La Liga champions linked to the player in October, according to Albert Gracia of Sport. Like their rivals, Real also have a fine left-back in Marcelo but could still use a player with Alaba's versatility and athleticism.
Real could have the bigger need, especially since Valverde has Mina, Digne and Thomas Vermaelen, who can all play at more than one spot on the left side.
If Spain's two biggest clubs do go head-to-head for one of Bayern's prized assets, Barca's current standing may help them win the race, though. The Camp Nou club is top of La Liga, 19 points clear of Real, who face a fight for fourth place and qualification for next season's UEFA Champions League.