Earnhardt, who announced Thursday he could not race this weekend at New Hampshire Motor Speedway because of the symptoms, missed two races in 2012 because of concussions.
The 41-year-old Earnhardt believes crashes June 12 at Michigan and July 2 at Daytona possibly caused the symptoms, which he initially thought were from severe allergies or a sinus infection.
"He and I talked about years beyond next year just around Daytona," Hendrick said Sunday afternoon at NHMS, referring to Earnhardt's contract, which ends in 2017. "If there was something major wrong, I think they would have seen it already.
"I'm very hopeful and he's very hopeful. I think the doctors want to err on the side of being sure. We want him for a long time."
Alex Bowman replaced Earnhardt at New Hampshire and had a solid day ruined when he hit the wall late and finished 26th. He was running in the top-10 when he had contact on a restart at lap 269. Four laps later, a fender rubbing a tire as a result of the contact ended up in a flat and a crashed into the wall.
"I"m really disappointed to end our day that way but we showed we were a top-10 car all day long," said Bowman, whose career-best in 72 Sprint Cup starts is 13th. "It was the first time I've really run top-10 in a Cup car. We made a lot of progress this weekend. It is by far my worst race track, so to come here with these guys and run that well just shows what a great piece they bring to the race track."
Jeff Gordon will come out of retirement to replace Earnhardt if he cannot compete July 22-24 at Indianapolis Motor Speedway. Hendrick said that Gordon, a four-time Cup champion who moved from racing to the Fox Sports booth after last season, could do more races.
"Hopefully Dale is going to be back next week and it's not even something we think is going to happen," Hendrick said. "Jeff is a team player and wants to support the organization, and I'm sure he'll do whatever he has to do."
Hendrick said he was busy lining up an ear, nose and throat doctor for Earnhardt last week before Earnhardt's visit to the neurologist indicated he should sit out the New Hampshire race.
"He's running through a bunch of tests, and he's going to have some more tests the first of the week," Hendrick said. "He's doing good. He wants to be in the car. The doctors are going to tell him when it's OK for him to be back.
"I know he's anxious, and we want him back as soon as the doctors give clearance."
Hendrick said he didn't notice anything about Earnhardt that would indicate he was suffering from a concussion after the Michigan race. He said he doesn't know if any of his drivers are hurt unless they tell him, and the first he heard of the symptoms was last week. He said he believes the drivers do the right thing and let the teams know if they are hurting.
"I've had enough sinus infections, and when you're taking medication for that, you don't feel 100 percent," Hendrick said. "That was it."
For Earnhardt to be eligible for a Chase for the Sprint Cup berth, he would need a waiver to have missed a race during the regular season. It is expected he would get one, but Hendrick said he hasn't even applied for one yet, as the focus remains on Earnhardt's health.
By missing the race, Earnhardt dropped from 14th to 16th in the Chase-qualifying standings, with his cushion on the first driver outside the provisional Chase cutoff, Trevor Bayne, dropping from 32 points to 14 points.
"He's kind of an iron man -- he doesn't want to let the team down, he doesn't want to let his fans down," Hendrick said. "We need him for the long pull. He wants to be in the car. But the best thing the doctors can do is go through all the protocol and do all the tests, and there's a bunch of tests.
"When they say, 'You're good to go,' he'll be back."
The team already had Bowman in place as a backup for New Hampshire and stuck with that plan to keep him as the full substitute driver. Gordon, who is still an equity owner in Hendrick Motorsports, was in France last week when Hendrick called him.
"He thought I was kidding at first," Hendrick said. "He was on vacation and I asked him what he was doing and he said, 'I'll be in Indy.' ... I said, 'Bring your driver's uniform just in case.'
"He said, 'Are you kidding?' I said, 'No, I'm serious.'"