The Manchester Evening News says United coaching staff feel he has stepped up his training at Carrington amid competition from Henderson.
The presence of Henderson, 23, has prompted the United goalkeeping coach Richard Hartis to modify De Gea's warm-up before games in that he is now tasked with pinging passes to Henderson on one wing and third-choice 'keeper Lee Grant on the other flank. Henderson executed such a pass on his United debut against Luton Town and De Gea's distribution has drawn criticism in recent years.
United have shipped 11 goals in their first three Premier League matches but De Gea has not been directly blameworthy for any of them.
Manager Ole Gunnar Solskjaer has stayed loyal to the United number one but De Gea's positioning was awry for Ukraine's winner against Spain in their Nations League encounter in midweek.