Hales, 30, was dropped from England’s World Cup squad in for an “off-field incident”. The Guardian reported he had failed a recreational drugs test.
He had previously been suspended over his part in an altercation outside a Bristol nightclub in September 2017.
“The door isn’t closed. He’s a very fine short-format player,” Giles said.
“In the immediate term, he hasn’t played a lot of Cricket this year for us for different reasons and, as [captain] Eoin Morgan has said, there’s a certain amount of trust that needs to be gained back.
“He needs to keep working hard and getting the runs – but if he does that, who knows?”
At the time, Morgan confirmed that Hales’ omission was endorsed by senior players because of what he described as a “complete breakdown in trust” between the Nottinghamshire batsman and the rest of the squad.
Giles wants new coach in next month
Giles also said he intended to appoint one head coach to replace the outgoing Trevor Bayliss, who oversaw World Cup glory and a drawn Ashes series over the summer.
The former England spinner said he hoped to have someone in place before the players leave for the tour of New Zealand on 21 October.
Giles, who also appointed Australian Bayliss in 2015, said: “I see one coach leading the whole thing. I’ve been part of set-up where there are two coaches and role-playing that out, for me, it doesn’t end particularly well.
“If we have one head coach and some very good assistants, we are going to have to look after those guys well. The head coach would have some time off, so it’s an opportunity for those assistants to lead in different forms.
“I hope we have a shortlist in a week to 10 days and we will go through interviews. We won’t rush it but it would be nice to have someone in place before we leave for New Zealand.
“It will be a global list. We will search far and wide for the right candidate.”
Stokes ‘not affected by newspaper story’
Giles also said England’s Ben Stokes was owed an apology by a newspaper which printed an article about his family, leading to the all-rounder releasing a critical statement.
Stokes has called the Sun’s front-page story on Tuesday “utterly disgusting”, though the newspaper has defended its journalism.
The 28-year-old hit a match-winning innings in the World Cup final, and then struck an unbeaten 135 in the third Ashes Test against Australia in August to keep England in contention in the series.
“The article was unnecessary and the timing was poor,” Giles told BBC Sport. “It was misjudged because over the last six months Stokes has become a national hero.
“I hope the newspaper regrets it. The best thing it could do is apologise to the Stokes family.
“As for Ben, he is rock-solid, he is one of our warriors.
“What was fantastic to see was how his team-mates and management rallied round him and his family, and the wider public and other people from sport and TV and beyond.”