Modric has impressed for both Zagreb and his country over the past few years, but as yet no big-money offer has sufficiently tempted Dinamo to sell.
However, it has now been reported that Chelsea owner Roman Abramovich has started negotiations for his signature, with speculation suggesting Dinamo's vice-president Zdravko Mamic visited England this week.
And now a member of the club's management committee, Tomislav Marcinko, has confirmed Abramovich is vying for their prized asset.
"Abramovich is ready to pay for every one of Modric's kilos," he told The Observer.
Modric will be handed opportunity to prove his has the physical attributes to handle the demands of English football, when he travels with the rest of Croatia's squad for Wednesday's crucial Euro 2008 qualifier at Wembley.