Police wanted to interview Eddie Lyons Jnr over the gangland hit - and claims that he had been shot by Carroll just days before the murder.
Cops swooped on his mother-in-law's home when it was claimed he had returned to Glasgow and his BMW X5 was seen outside the house.
But there was no trace of Lyons Jnr, who was reported to have fled to Spain after Carroll was killed.
And his wife Joanne, who was visiting her mother, claimed not to know where her husband was.
Underworld sources say Carroll, an enforcer for the rival Daniel crime clan, had shot Lyons days before he was gunned down in an Asda car park.
It is claimed two shots hit Lyons Jnr's bulletproof vest while a third struck him on the arm.
And gangland insiders say that was the trigger for Lyons Jnr to order Carroll's execution.
Cops also want to quiz Lyons Jnr's brother, Stephen, 29, who is based in Spain.
On Friday afternoon, rumours began to circulate that Lyons Jnr had returned to Glasgow to see a close family member who is seriously ill.
Cops were tipped off that a black BMW believed to belong to Lyons Jnr was outside his mother-in-law's home in Milton, north Glasgow.
Members of Strathclyde Police's Gangs Task Force were scrambled to the scene and were joined by detectives probing Carroll's murder.
An underworld source said: "The police were at the house within minutes of being tipped off about the X5 but Eddie was nowhere to be seen.
"There were a number of people in the house, including his wife, but they all pleaded dumb as to his whereabouts.
"Everything points to the Lyons family having a hand in Gerbil's murder and the word on the street is that Eddie Jnr sanctioned the hit.
"The cops are desperate to catch up with him."
Last week, we revealed another leading member of the crime clan, David Lyons, has not been seen at his garage since Carroll, 29, was gunned down outside Asda in Robroyston on January 13.
David Lyons's garage in Lambhill, north Glasgow, has already witnessed a triple shooting which left his nephew, Michael Lyons, dead.
Stephen Lyons and a third man, Robert Pickett, were also shot but survived.
Sources told us David is taking no chances of a repeat of the December 2006 attack, which was likened in court to a scene from The Godfather.
David's son Mark has also not been spotted at Applerow Motors in north Glasgow since Carroll was murdered.
The garage remains operational and sources claim it has been busy in recent weeks.
David has always claimed he is a legitimate businessman but police intelligence revealed in 2007 that he was "involved in serious and organised crime, including the trafficking and supply of Class A drugs".
More than 10 shots were fired at Carroll as he sat in the back of a black Audi outside the supermarket.
The three-man hit squad then sped off in a dark blue Volkswagen Golf, which was found burnt out.
A fortnight after the hit, two guns were found dumped in Coatbridge and tests confirmed they were the murder weapons.