Per Bills coach Sean McDermott, Allen and Nathan Peterman will rotate turns working with the first-team offense. Peterman, who had that honor on Sunday, was slated to work with the second team on Monday.
Fellow quarterback A.J. McCarron was injured during the Bills' preseason game against the Cleveland Browns on Friday.
The Buffalo News previously reported that the 27-year-old received a hairline fracture in his collarbone. McDermott said Sunday that McCarron did suffer an injury but that tests are "not totally conclusive" before acknowledging that the quarterback will go for another medical opinion.
"Like always, (Bills general manager Brandon Beane) is always looking at our situation and what we may need to do for not only the long term, but the short term in this case. We'll see," McDermott said, per ESPN.
Allen, who was the seventh overall pick of the 2018 NFL Draft, replaced McCarron and led the Bills' first-team offense on an 80-yard touchdown drive in the second quarter against the Browns.
While playing three possessions, Allen completed 9 of 13 passes for 60 yards and a 2-yard touchdown pass to wide receiver Rod Streater.
The 6-foot-5, 237-pound Allen passed for 1,966 yards with 19 touchdowns last season at Wyoming. He ran the 40-yard dash at the NFL Scouting Combine in 4.75 seconds with a 33 1/2-inch vertical jump.
Peterman took over from Allen early in the third quarter and closed out Friday's game, completing 8 of 10 passes for 113 yards.
"We're just with the rotation at this point," McDermott said. "We'll make that decision. After today, we'll start to move into a little bit of a blend of (this being) a normal week as we prepare. Our players can get acclimated to the routine of a normal, regular season week."
The Bills return to preseason game action on Sunday against the Cincinnati Bengals.