A Rijeka-based radio station are confident the 23-year-old has agreed a move to the Foxes, costing the Premier League strugglers £9.5m.
The Croatian hitman has been sceptical about joining Nigel Pearson's side due to their position at the foot of the table, but has seemingly been assured he will be sold should the club lose their top-flight status in the summer.
Leicester have reportedly offered Kramaric - who has bagged 28 goals in 30 outings this term - a weekly wage of £28,000.
The report claims: "Andrej Kramaric has travelled to London with his father and agent Joza Kramaric along with Rijeka's Managing Director Ivan Mance, where he will have the last round of negotiations with Leicester City.
Andrej Kramaric has travelled to London where he will have the last round of negotiations with Leicester City
"If nothing changes until tonight or early tomorrow, with a transfer fee of €12m (£9.5m) to be paid to Rijeka.
"That offer was sent 15 days ago but was refused by Kramaric as he wanted to sign for a stronger side than Leicester.
"But after a couple of meetings with Rijeka's chairman Damir Miskovic, Kramaric has changed his mind and agreed to Leicester City's offer.
"Reports state his salary will be close to €1.5m (£1.15m) per season and also say Leicester City will be prepared to sell him in the summer window should they get relegated from the Premier League."