Officers have been given seven more days to question three men, two aged 26 and one aged 40, and a 29-year-old woman - all from Birmingham.
All four are being held under the Terrorism Act.
A fourth man, aged 59, has been freed on bail "with strict conditions".
Four of the people were arrested in Birmingham on Thursday, while one of the 26-year-old men was arrested at Gatwick Airport in the early hours of Friday.
The group of four are still being held in the West Midlands, where they continue to be questioned by officers.
Searches continue at a number of properties in Birmingham as part of the investigation, West Midlands Police said.
Police said the arrests were made after they worked with MI5 and Belgian and French authorities.
They said there was no risk to the public at any time and they had no information to suggest an attack in the UK was being planned.
West Midlands Police has previously refused to confirm reports that images of landmarks in Birmingham, including a shopping mall, were found on a mobile phone belonging to one of the alleged Paris ringleaders.
Police have been given more time to question four people arrested on suspicion of terrorism offences as part of an investigation launched after the recent attacks in Paris and Brussels.