The former manager - who took the club to second in the league and within a missed penalty of the Champions League in 2008 - is a friend of Abramovich, and according to assorted reports on Monday, will be offered a consultancy role at Chelsea.
Both The Guardian and The Daily Mail report that Abramovich fears his appointment of Rafa Benitez could be going wrong already, but that Grant - who apparently has a good relationship with the Spaniard - may help steady the ship.
The Mail claims Abramovich made a personal visit to the Chelsea training ground last week, and also invited a small group of fans to his office to discuss Benitez's appointment.
However, The Guardian believes bringing back Grant would further sour relations with the club's support.
The paper reports: 'The Israeli's return to the club would represent further antagonising an increasingly disillusioned fanbase, though that he is under consideration reflects the chaos currently gripping the European champions.'
Benitez said he was angry after Chelsea's defeat to West Ham at the weekend, comparing his current squad unfavourably to the one his old rival Jose Mourinho had at his disposal.
Benitez said: "Normally when you lose, you are not happy - but I was angry. We did not manage their physical game, the long balls, the second balls, the corners.
"We gave them too many options to play their game and we could not be comfortable in possession.
"That is when you have to show character and quality - and we did NOT do that.
"Character and leadership is always necessary in a team.
"Jose Mourinho's Chelsea team had a lot of character but it is a different time now."