The French giants are keen admirers of the former Monaco start, who initially struggled to settle in England t has shown glimpses of his real quality in recent weeks.
However, Spiro, insists all is not well in the Fabinho camp and that PSG could still lure him back to France in January – albeit on an initial loan deal.
Spiro also claims they are also considering Everton’s Idrissa Gueye and Cesc Fabregas from Chelsea as they look to strengthen in midfield.
Ajax sensation Frankie de Jong is another target but that will probably have to wait until the summer.
“#PSG are talking to Idrissa Gueye’s representatives about a possible January move,” Spiro said on Twitter.
“French champions need an extra man in the middle. Fabregas or Fabinho (on loan) being considered. De Jong remains a summer target.
“Doubt #LFC will let Fabinho go in Jan, but anybody thinking everything’s ok here is being very naive.
“The ‘he needs time to adapt to English football’ rhetoric is nonsense.
“He’s more than ready, has been for months, and can’t be happy starting just 6 league games.”
Fabinho put in arguably his best performance in a Reds shirt in the recent 3-1 victory over bitter rivals Manchester United.
The Brazilian, 25, set up Sadio Mane for the opening goal and his versatility could be crucial as manager Jurgen Klopp deals with injury problems and a hectic schedule over Christmas.
Fabinho is equally adept at right-back as he is in the centre of midfield and Klopp even hinted he might fill in at centre-back when they travel to Wolves in the Premier League on Friday night.
He goes into the game without Joe Gomez or Trent Alexander-Arnold, while Dejan Lovren is a major doubt.
“I hope Dejan (Lovren) can play them all but I don’t know in the moment. It looks really good,” he said.
“We don’t really have options. But Fabinho can play at centre-half as well so that’s good.”