The 'Daily Star' is claiming that the quartet of top clubs did not want the Spaniard.
It is thought that the midfielder is not in Antonio Conte's long-term plans and that the Italian was trying to offload the former Arsenal and Barcelona man.
Fabregas joined Chelsea in 2014 from Barcelona where he enjoyed a successful first season for the club, winning the Premier League title.
However, the 29-year-old was part of a Chelsea side that struggled last season and will face added competition for a place in the side with the arrival of N'Golo Kante.