Five people were arrested at the weekend, but at least one suspect is still believed to be on the run.
Those held so far include a qualified medical doctor. Police say none of the suspects is British in origin.
Police are linking the failed bombings and the UK remains on high alert amid fears of a possible further attack.
The terror alert level was raised to critical - its highest level - after a Jeep Cherokee, loaded with gas cylinders, crashed into the doors of Glasgow Airport's main terminal and burst into flames on Saturday afternoon.
Not intimidated
Alex Salmond, Scotland's First Minister, told BBC Radio 4's Today programme that life was already getting back to normal in Scotland.
"The prime minister and I have been at one in making sure that the country will not be intimidated or stopped from going about its business by terrorist incidents," he added.
The attempted attack in Paisley came a day after two Mercedes containing petrol, gas cylinders and nails were found outside a nightclub in London's Haymarket and in a nearby street.
The devices failed to detonate.
Commuters and air travellers are being warned to expect extra delays to journeys on Monday, with extra police patrols and vehicle searches taking place at airports and transport hubs.
Detectives are trying to trace the movements of the green Jeep Cherokee - registration L808 RDT - which crashed into the airport.
BBC home affairs correspondent Danny Shaw suggested the need to track the vehicle's movements could mean the police were still not sure where the car bomb's components were picked up and assembled and who else was involved.
Five people have so far been arrested in connection with the two incidents - in Glasgow, Liverpool and Cheshire.
A 26-year-old man and 27-year-old woman were arrested on the M6 near Sandbach, Cheshire, on Saturday night.
The man has been identified by the BBC as Dr Mohammed Asha.
Both have been taken to Paddington Green police station in London for questioning.
Their arrests are linked to the search of a house at Newcastle-under-Lyme in Staffordshire.
Another 26-year-old man was arrested in Liverpool on Sunday and remains in custody at a Merseyside police station.
Two men were detained at Glasgow Airport on Saturday after the attempted attack.
One had severe burns and remains in a critical condition, and under armed police guard, at Royal Alexandra Hospital, in Paisley.
The BBC has learned those arrested are believed to be of varying Middle Eastern nationalities.
On Sunday, police also searched addresses in the Liverpool area and in Houston, Renfrewshire, close to Glasgow Airport.
The UK's top counter-terrorism officer, Deputy Assistant Commissioner Peter Clarke, of the Metropolitan Police, said the links between the three attempted car bombings were becoming "ever clearer".
Fast-moving inquiry
He described the investigation into the failed bombings as "extremely fast-moving".
"It is no exaggeration at all to say that new information is coming to light hour by hour," he said.
He said forensic searches of vehicles were proving "extremely valuable" and thousands of hours of CCTV were being sifted through.
In other developments: