The England international picked up the injury during a training session last month and was expected to make a return to the field by November.
Despite initially being on course to recover, the medical team at White Hart Lane are not planning on rushing the 27-year-old back into action.
"I was outside running earlier in the week but the Achilles was still a little sore, so I've had to take a step back and concentrate on working in the gym," Dawson told the club's official website.
"The physios aren't too worried as I've been in a protective boot for a couple of weeks and I need to strengthen it up.
"I'm obviously a little down, but you never know with injuries and rehab, so we'll wait and see."
The London side travel to Newcastle in the Premier League after the international break on October 16.