It is understood the 22-year-old midfielder, accompanied by Dinamo Zagreb vice-chairman Zdravko Mamic, was on Tyneside on Tuesday to discuss a prospective move to St James' Park.
Modric visited the club's Darsley Park training headquarters after holding talks with executive director (football) Dennis Wise and vice-president (player recruitment) Tony Jimenez at the stadium.
Reports from Croatia have suggested the left-sided player is on the verge of completing a £20million move to Newcastle, although Dinamo value him at some £5million in excess of that.
Either fee would smash the club record £17million they paid for England striker Michael Owen almost three years ago, and it remains to be seen to what extent owner Mike Ashley is prepared to fund manager Kevin Keegan's rebuilding programme.
The club's negotiators would hope for some movement on the asking price, although the player's wage demands too are likely to be significant.