Only this week, Fabregas told Movistar: 'People talk a lot but the truth is that no-one has spoken with me.
'I want to triumph in Barcelona, that club is my home and I always dreamed of playing there, so I will try and succeed there as long as I can.'
Moyes has held a long standing interest in Thiago, who illuminated the recent European Under 21 Championships, but hasn't had the financial muscle at Everton to engineer a move. United, too, have been on the 22-year-old's trail since his late teens.
The son of Brazilian World Cup winner Mazinho has grown frustrated with his lack of playing time at the Nou Camp since 2011, and it is that shortage of action which means he is available for a cut-price £15million.
When he signed a new deal two years ago, a clause was inserted which stipulated the midfielder must feature for at least 30 minutes in 60 per cent of matches. He however fell short of that time on the pitch in 15 of his 36 appearances.
As Barca failed to give Thiago, who scored a hat-trick in Spain U21's final win over Italy on Tuesday, his designated playing time, his release fee dropped from £77m to a far more affordable £15m.
Despite the interest from his former club, Gerard Pique has urged his new team-mate to stay with the La Liga champions.
He said: 'There is a possibility that he could leave but we have to convince him that the best place for him is Barcelona.
'Players in his position like Xavi were patient and they ended up defining an era.'