The defender has been forced to sit out the last two matches against Ipswich Town and Sheffield Wednesday due to a foot injury.
The Bees have coped reasonably well with Ajer's absence, claiming a 4-3 Premier League win over Ipswich before beating Sheffield Wednesday on penalties to set up an EFL Cup quarter-final tie with Newcastle United.
Brentford are now preparing for a West London derby, with the Bees set to make the short trip to Craven Cottage for Monday's clash with Fulham.
Brentford in line to receive Ajer boost
Frank has confirmed that Ajer is back in training and is hopeful the 26-year-old will prove his fitness in time for the derby clash.
"Kristoffer Ajer is progressing well," Frank told reporters in Thursday's press conference. "He has a big chance, and he has been in training."
Ajer has been utilised as a right and left full-back this season, and he could be considered for a starting spot if he is passed fit.
The Brentford boss also confirmed that midfielder Christian Norgaard will return to the matchday squad after being rested for the midweek cup tie against Sheffield Wednesday.
Who will miss Brentford's derby clash with Fulham?
While Ajer and Norgaard could be in contention, Frank is still having to cope with several absentees ahead of Monday's fixture.
Rico Henry and Igor Thiago are both sidelined with knee injuries, while Gustavo Nunes is still recovering from a back problem.
Full-back Aaron Hickey and midfielder Josh Dasilva are both long-term absentees due to hamstring and knee injuries respectively.
Frank will hope that those available for selection can claim a positive result after seeing his side lose all four of their away league games this season.