Gordon retired at the conclusion of last season and served as a television analyst for the Fox Sports portion of the 2016 NASCAR schedule.
Duchardt said Hendrick could wait until Wednesday next week to decide whether Earnhardt or Gordon would race at Indianapolis and has not planned beyond that.
Earnhardt will sit out Sundays race at New Hampshire Motor Speedway and there is no timetable on when NASCARs most popular driver might return.
Earnhardt missed two races in 2012 because of two concussions over a six-week period. Consider also that Gordon has five victories at the Brickyard, a record for the vaunted track.
Duchardt also said their main concern is that Earnhardt Jr.is 100 percent before he climbs back into the auto - no matter how much time it takes.
"On Tuesday morning, he (Dale) notified Greg (Ives) and me before our competition meeting, that he still wasn't feeling real well", said Duchardt. And obviously the way the week went, we didn't even think we were going to need a replacement driver. The New Hampshire race will be the third he has missed in his 17-year career.
Upon his retirement, Gordon didn't rule out driving occasionally in selected events or other series, but his possible return in the Cup Series at one of the sport's iconic speedways is a scenario few could have expected.
Gordon, 44, is an equity partner in Hendrick Motorsport.
Earnhardt is winless this season and 13th in the points standings. Gordon is vacationing in France.
"As far as Jeff Gordon's situation, certainly he's a four-time champion with 93 wins".
"I'm looking forward to treatment with the goal of getting back in the race vehicle when the doctors say I'm ready", Earnhardt said. "But if Dale can't go next week, Jeff Gordon will be the driver at Indianapolis".
Dale Earnhardt Jr., like many veteran NASCAR drivers, is no stranger to hard crashes and head injuries similar to what football players endured before being diagnosed with chronic traumatic encephalopathy (CTE) post-mortem. Concussed drivers must be cleared by a neurologist or neurosurgeon before they can get back in a race vehicle.
Earnhardt experienced concussion-like symptoms following crashes at MI and Daytona.
On Thursday, HMS officials announced that Earnhardt had not been cleared by doctors to compete this weekend, and that Alex Bowman would replace Earnhardt in the team's No. 88 Chevrolet.