The Swede who is expected to be sacked by Manchester City at the end of the season is the number one choice of Chelsea chief executive Peter Kenyon to replace the underfire Grant.
It was with the former England coach that Kenyon and cohorts held secret talks about becoming Chelsea coach a couple of years ago.
Once pictures of the meeting were beamed around the world, Chelsea's interest cooled.
But with Eriksson viewed as having a successful season at City, which included doing the double of rivals United, he is back in favour.
Grant took over at the helm at Stamford Bridge, replacing Jose Mourinho in September.
But he has not won over the fans nor senior members of the Chelsea set-up and he is expected to be rewarded for his efforts this season by being offered his former job of director of coaching.