The 23-year-old Argentine has now played an hour of pre-season football as he stepped up his recovery from an 18-month injury lay-off against Histon.
He told the club's website: "My return is going better than I thought.
"If I carry on as I am I will be ready for the start of the season. If not the start, then two or three games in."
Civelli had been sidelined since March 2009 when he suffered extensive knee ligament damage during a league game against Burnley.
I always tried to stay positive and I'm happy with the progress
Ipswich Town winger Luca Civelli
He played 30 minutes in Town's first pre-season friendly of the summer, a 9-1 win over Newmarket, and then played another half an hour as Histon were beaten 6-0.
"I have been a long time out injured but it's good to be back playing football again and I am happy with how things are going," he added.
"When you are injured for a long time you worry sometimes about whether you will come back but I always tried to stay positive and I'm happy with the progress."
Connor Wickham scored twice against the Stutes in his first pre-season outing while David Norris, Gareth McAuley, Lee Martin and Jonathan Stead added the rest.
Source: BBC Sport
Source: BBC Sport