The 63-year-old singer, who will arrive in Albert Square on Friday, grows closer to the Walford matriarch after heroically saving Roxy Mitchell's (Rita Simons) daughter Amy from the path of her car.
An insider told The Sun: "Eddie and Carol have a spark and she is delighted when he makes a move on her. The attraction is there but they both have too much on their plates to start a proper relationship for now.
"Eddie is desperate to build bridges with his estranged son Michael (Steve John Shepherd), although he's not interested in forgiving what's happened between them in the past and tries to pay him off to leave Walford."
The source added that Carol will struggle to find time for her newfound love following her on-screen father Jim Branning's (John Bardon) recent admission to a care home.
"Carol's also got a lot on her mind with her dad Jim going into an old people's home. There's every chance that things will develop between them in the future. But for now their relationship has to be put on a backburner because the timing isn't any good."
Commenting on the storyline, Coulson confessed to harbouring a real-life crush on the 'Hold Me Close' star during her teenage years.
"I went to all his concerts," she said. "Don't tell him - I was 14. He was lovely!"
The 63-year-old's EastEnders arrival will proceed that of his on-screen sons, new Moon brothers Tyler (Tony Discipline) and Anthony (Matt Lapinskas).
Watch the trailer for David Essex's EastEnders debut below.