The 33-year-old Warwickshire left-armer will miss the May/June series against Sri Lanka after undergoing surgery and is one of several key England players to have suffered injury since the team's Ashes success over Australia last year.
''It has measurably improved over the last three days and I'm already back on the exercise bike at home,'' Giles, who has also been bothered by a hip problem, told yesterday's Daily Mail.
''They told me I could be back running within a fortnight and I can see that happening. I'm not setting targets, but six weeks to be back playing again in some form feels like it's realistic,'' added spinner, who had surgery last week following a lengthy diagnosis period.
''With hindsight, I probably should have had the hip done before I went to Pakistan. Looking at footage of my bowling action towards the end of last summer it's obvious that I wasn't putting any weight through my front leg,'' he said.
''I'm feeling positive about it, although the underlying issue is still the hip and we may find that there is still something going on there.
''The hernia is a footballer's injury and we have been in touch with the people at Arsenal about it. So far it's all going to plan.'' After a long apprenticeship, Giles has developed into a useful spinner for England and is now rated as something of an all-rounder having chalked up an average of almost 25 in his last 20 Tests.
As a key member of the Ashes-winning team, he is obviously keen to return to the side in time to defend the urn in Australia at the end of the year.
However, having already been ruled out of the Sri Lanka series, which begins with the first Test at Lord's starting on May 11, he is targeting a July international return.
''I just want to try to be available for the Tests against Pakistan this summer. If everyone gets fit again we may come to look back at what has happened to us in the last six months and it will make us stronger,'' he said.
''It has been hard being out of the side and, as a 33-year-old, you just want to be out there doing what you are paid to do.'' Pacemen Steve Harmison and James Anderson have both been ruled out of next week's opening Sri Lanka Test, while Simon Jones is also an injury concern after he picked up a knee injury on Monday.