The 26-year-old defender still has two years left of his current deal to run but negotiations on a new contract were believed to have reached a sticking point over the central defender's wage demands.
"It is very promising and I am hoping things can be done," Terry said. "It has moved a step closer.
"We have spoken since we have been here and we have moved closer. Aaron is over here, not only for that but hopefully things can be done before the start of the season."
Terry insisted that negotiations with the club had not stalled.
"It has not dragged on. These things take time.
"I said at the end of the last season that it was important to finish the campaign.
"We won the FA Cup and I wanted to get away and have a complete break with my family and I've done that.
"I've come back and we are speaking again. These things don't happen overnight.
"It is a case of minor details that need to be looked over not only by myself but by solicitors from my end, from Chelsea's end."