The Magpies recently saw Leicester turn down a bid for Maddison, which came in at the £40m mark, but they are not giving up the pursuit.
It is suggested that Newcastle have been told that Maddison would like to make the move to St James’ Park this summer and they are trying to agree a fee with Leicester.
They have now gone in with a fresh proposal which comes in at in excess of £45m.
However, the payments in the deal are staggered and it remains to be seen if Leicester will feel that it is acceptable for a player they want to keep.
Maddison has another two years left to run on his current contract at the King Power Stadium.
He made 53 appearances for Leicester over the course of last season, scoring 18 goals in the process.
Newcastle believe Maddison could slot in under Eddie Howe and flourish at St James’ Park, but it is far from clear whether they will get their man.
