The Norwegian defender was thought to have been in with a good chance of coming back from a foot injury in time for the trip to Fulham on Monday, but he was ultimately not involved as the Bees slumped to a 2-1 loss.
However, the extended recovery time should give Ajer the best possible chance of returning to the left-hand side of the backline in Rico Henry's absence, as the long-term knee victim is unlikely to be risked just yet.
Igor Thiago (knee), Josh Dasilva (knee), Aaron Hickey (thigh) and Gustavo Nunes (back) are also taking up beds in the Brentford infirmary, but Ajer's comeback may allow Sepp van den Berg to revert to a right-back role as Mads Roerslev drops out.
Ethan Pinnock and Nathan Collins are shoo-ins ahead of Mark Flekken, and the same goes for Christian Norgaard and Vitaly Janelt - scorer of a fine opener at Craven Cottage - in midfield.
Mikkel Damsgaard is poised to operate just ahead of the duo once again, providing support to what should be an untouched attacking setup of Keane Lewis-Potter, Bryan Mbeumo and Yoane Wissa.
The latter is on a four-game scoring sequence in Premier League home games, while Mbeumo has made the net bulge in each of his last five top-flight matches at the Gtech Community Stadium.
Brentford possible starting lineup:
Flekken; Van den Berg, Collins, Pinnock, Ajer; Damsgaard, Norgaard, Janelt; Mbeumo, Wissa, Lewis-Potter