Such a claim is made by Spanish publication Marca, who cite both personal and professional reasons for this - including the fact that the Red Devils will not partake in the Champions League next season after a dismal spell under the management of David Moyes.
The newspaper also points to Frank Lampard's exit from Chelsea, which would seemingly afford Fabregas the opportunity to secure regular first-team football in West London - something he is far from guaranteed during a period of notable transition with current club Barcelona.
Whether Barcelona would be content to sell him to Chelsea remains to be seen, however, as does the stance of Blues boss Jose Mourinho on the possibility of such an arrival given that the relationship between the Portuguese and Fabregas has always appeared somewhat fractious in the past.
Reports earlier this week claimed that Fabregas - who is rated by Barcelona at around the £29.2 million mark - may already have had a medical at Chelsea which, if proved correct, would come as a crushing blow to the other English teams who have been frequently credited with a strong interest in pursuing the Spain international.
The seemingly never-ending avalanche of speculation concerning Fabregas' future is coming at potentially the most unsettling time, with the 27-year-old - whose previous experience of the Premier League came in a successful eight-year stint with Arsenal between 2003-11 - currently preparing for Spain's upcoming World Cup title defence in Brazil.
It is something that Fabregas should be able to cope with by now, however, with the player having become the subject of a similar saga last summer, when then Manchester United boss David Moyes was believed to be chasing his signature.
Manchester United's interest in Fabregas does not seem to have waned since former Barcelona manager Louis van Gaal was announced as Moyes' successor, but it still appears as if the club's chances of finally landing him are slim in the face of rather stiff competition.
Chelsea fans - would you like to see Fabregas arrive at Stamford Bridge? Do you believe he and Mourinho - two undoubtedly fiery characters - could peacefully co-exist inside the same dressing room or would you prefer the club to look elsewhere in their pursuit of an adequate replacement for Lampard? Let us know your thoughts in the comment box provided below.