Detectives made inquiries about his whereabouts last week, the first time since the BBC tracked him down to Spain in March. Garda sources declined to say whether fresh complaints have been made or if he would be arrested.
However, the Murphy report said he was suspected of abusing at least 32 children and it is believed that others would have come forward since the report was published.
The Garda interest in Carney coincides with the ex-priest's return to the UK after hiding out in Spain since the report's publication.
Since his past was exposed, his wife has left him and the ex-priest has claimed to friends that he was left penniless in Spain. The guest house they ran together in St Andrews in Scotland has been sold and Carney is now after his share of the proceeds.
Paul Clayton, whose mother married the ex-priest a number of years ago, said he released some funds to enable Carney to fly back to England. Once back in England, Carney used a friend's hotel in Stoke-on-Trent to contact solicitors for the Claytons to seek his share of the proceeds.
"The gardai have been in touch with me asking for his whereabouts and they also said they will ask the English police to investigate," Mr Clayton said.
The priest left Ireland after he was thrown out of the priesthood in 1992. He set up a new life in Scotland.
In 1983, the cleric was placed on probation after admitting two counts of indecent assault against two altar boys. He was defrocked nine years later after a canonical inquiry found him guilty of abusing children. He refused to leave his parish house until he secured a pay-off of £30,000 from the diocese.
All the time, Carney was a member of the prestigious Royal Golf Club in Clontarf in north Dublin and featured on a plaque honouring its top golfers in 1994. Members recalled how he regularly arrived for a round of golf with children who caddied for him on the course.
Carney was expelled from the Royal Dublin in the mid-1990s after newspaper reports exposing his past and he moved to the UK.
His crimes were never passed on to the UK police. His crimes pre-dated the sex offenders' register which was only introduced in 2001.
He knew Joan Clayton for many years and they married about five years ago. He lied to her about his past, claiming that he was kicked out of the church because of his drinking.
Mrs Clayton was on holidays in Spain in December when the Murphy report was published. "As soon as I heard about it, I just flew out there and got her," Mr Clayton said.
The guest house, Amberside, was put up for sale with an asking price of £665,000.
In March, Carney was tracked down to Gran Canaria, where he told BBC Newsnight: "I have read the report six or seven times and would dispute all of it except that I have been convicted of two charges in 1983."
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