The 22-year-old was initially named in England's Six Nations squad, but he suffered a knee injury two weeks before the start of the tournament.
It is understood that Burns will be fit for Gloucester's clash with Bath Rugby on Friday, which would also place him in contention for England's final two Six Nations matches against Italy and Wales.
"It's back to square one for me. It was a big blow to get injured and miss most of the tournament. I'm available for the next two games but I'll only have one match before then to prove my fitness," he told BBC Sport.
"I haven't written off the Six Nations because I want to help the boys if needed, but firstly I need to get fit and then it's about performing for Gloucester on Friday.
"That's my focus at the moment. I'll sort out what I do for Gloucester and if it means a call-up for England, then great. If not, then I'll just keep working hard for the club."
Burns made his international bow against New Zealand last year.