According to reports in the Belgian media, one of them, identified by the federal prosecutor's office as 29-year old Jawad B, is the nephew of Ibrahim El Bakraoui, one of two brothers who took part in the March suicide attacks.
Belgian state television station RTBF said Jawad B is Jawad Benhattal, who was the getaway driver of a failed robbery of a Western Union office in 2010 that also involved Bakraoui.
Both Benhattal and Bakraoui served time in prison for their role in the crime. Another of the detained men was named by RTBF as a 40-year old Moustapha Benhattal, who was also cousin of the El Bakraouis.
The links add to growing concern about the threat that Brussels may have been under in recent days, with indications that police were concerned about a possible attack on supporters gathered on Saturday afternoon to watch Belgium play Ireland in the European football championships.
Thousands watched the game at big screens across the city.
The anti-terror crackdown involved over 40 coordinated raids on Friday night and early Saturday morning in 16 of Brussels' 19 municipalities.
A total of 12 people were arrested, with nine released later on Saturday. Federal prosecutors said they had obtained intelligence that required "an immediate intervention".
In other security scares, Centrale Station in Brussels and the Europaplein, in front of the main entrance, were evacuated on Saturday after the discovery of two abandoned suitcases.
The bomb disposal unit DOVO examined the suspicious cases and rail services were suspended for about half an hour, said, Peter De Waele, of the federal police.
While trains were first allowed to pass the station without making a stop, services were later suspended and no-one was allowed to enter the station. The scare turned out to be false alarm.
Meanwhile on Monday, the Brussels public transport company MIVB said it had closed a number of entrances to six of its metro stations. The move has come at the request of the police and is for security reasons, it said.
MIVB spokesman Guy Sablon told VRT news that "this definitely doesn't mean that the stations themselves are closed but rather that just a few entrances to them are".
The closure of the metro station entrances is part of a series of measure that were announced by Belgian Prime Minister Charles Michel after Saturday's meeting of the National Security Council.