A file is now being prepared for the DPP and the suspect can be rearrested if new information comes to the investigation, particularly the discovery of her body.
The suspect -- a local man who had a brief relationship with Aoife and who comes from a respectable family -- was held by officers from around 4pm on Monday after returning to Ireland from abroad.
The man is expected to be placed under surveillance by gardai in the coming days as they try to build a case that can be prosecuted in court.
A source told the Herald: "Without the discovery of a body, it will be very hard to press charges in this case."
Gardai believe Aoife was beaten to death and her body thrown over a bridge and into the fast flowing river. Garda divers have been trawling through the waters.
A separate search at a house on the Timahoe Road in which a digger had been brought in to excavate land at the property went on for about four hours.
This property remained sealed off by officers today.
Forensic specialists have also been examining a 4x4 vehicle, which was seized by gardai on Sunday, as well as Aoife's handbag and mobile phone, which were also recovered as a result of their inquiries.
An examination of calls and texts made on Aoife's phone and on another mobile seized during the investigation showed that there had been a lot of traffic between the two on the evening of her disappearance.
Gardai were already aware from interviews with the friend that Aoife had met on Thursday week that she had been in contact with somebody on her phone.
She was last seen alive at 8.10pm, when she left her friend's house at Colliers View, apparently to meet the person who had been in contact with her through her mobile phone.
It is understood that this man, who had threatened her in the past, had told her he had car trouble and asked her to meet with him.