Delap, who joined from Ipswich Town for 30 million pounds in June, was injured against Fulham before the international break and initially it was expected he would miss six to eight weeks.
"It's around 10 to 12 weeks," Maresca told reporters.
Better news for Chelsea is that Cole Palmer, who was ruled out of the England squad because of a groin injury, is back in training and has a chance of facing Brentford.
"Cole took part in the session yesterday for the first time, not the entire session," the Italian said. "We have one more session this afternoon and we are going to try with him to see if he's okay, otherwise he will be out tomorrow.
"When he is available, we need to manage him because of the amount of games."
Chelsea will also likely hand a place on the bench to new signing Alejandro Garnacho, although Maresca said the Argentine winger was not yet 100% match fit after not playing this season before his move from Manchester United.
"He is working well. For sure, he needs to work because he arrived here not 100% fit," Maresca said.
"He needs to work. He is working well and we will see. Hopefully we can give him minutes."
Chelsea have begun the season well with seven points from three games, although this week the club was hit with 74 charges by the Football Association for alleged breaches of regulations covering football agents, intermediaries and third-party investment in players spanning more than a decade.
The FA said Chelsea had until September 19th to respond to the charge.
Maresca, however, played down any impact on the mood of the squad ahead of the return to Premier League action.
"I don't think the players are too worried about the situation," he said. "I know from the club that they are satisfied about the process. Personally, I have nothing to add.
"I have no idea, to be honest. I want to focus on the pitch, something I can control."