The singer is said to have met Gandy - best known for appearing in a Dolce & Gabbana advert - at an event last month.
A source told The Sun: "It's early days but so far, so good. They're having a really good time together. David's a few years older than Mollie but you can't tell."
King, who split from boyfriend of two years Andy Brown in February, cheered Gandy on as he ran the London Marathon last weekend.
Meanwhile, bandmate Frankie Sandford is dating footballer Wayne Bridge.
The band recently described their new single as "fierce".