Grant is available after leaving Partizan Belgrade in May and was on the short-list to replace Roberto Di Matteo after the Italian’s sacking in the wake of their Champions League defeat to Juventus.
The Israeli was manager of Chelsea during a tumultuous period and was sacked straight after reaching the 2008 Champions League final, though is still highly regarded by Abramovich.
Since then, the 57-year-old managed Portsmouth followed by West Ham United, a time during which he became the first man in Premier League history to run successive finishes at the bottom of the table.
Benitez, who has suffered intense hostility from the club's fans given his old ties with Liverpool, admitted over the weekend that he was not "100 per cent" of his future, following Chelsea’s woeful 3-1 loss to West Ham on Saturday – their third winless game.
"I am not 100 per cent. We didn't win today, and that is the main thing.
"I would say that it depends on the things that we can do on the pitch. So if we improve on the pitch, it will be easier for everyone.'"
The club are now 10 points behind Manchester United, with the loss at Upton Park extending their Premier League winless streak to seven games – their worst run since 1995.