Morris didn't draw a target while playing three of the Bills' 55 snaps on offense in Sunday's 34-10 win over the Titans.
Morris played nine of the Bills' 64 snaps on offense and didn't draw a target in Monday's 47-10 win over the Jaguars.
Morris (shoulder) will be a full participant during practice Wednesday, Chris Brown of the Bills Radio Network reports.
Head coach Sean McDermott said Thursday that Morris (shoulder) is trending in the right direction with his injury recovery and could be available for the regular-season opener against the Cardinals on Sept. 8, Alec White of the Bills' official site reports.
Coach Sean McDermott said Monday that Morris (shoulder) will miss multiple weeks due to an injury sustained during Saturday's preseason game against Pittsburgh, Alaina Getzenberg of ESPN.com reports.
The Bills re-signed Morris on a one-year deal Friday.
Morris went without a target while playing 18 of 68 snaps on offense in Sunday's 31-10 win over the Cowboys.
Morris (ankle) was a full participant in Thursday's practice.
Morris (ankle) will be a limited participant in practice Wednesday, Jay Skurski of The Buffalo News reports.
Morris (ankle) has been ruled out for Thursday's game against the Buccaneers.