Modric scored a superb solo goal in Croatia's impressive 3-0 win over Argentina and he was also on target, from the penalty spot, in the opening win over Nigeria.
The Real Madrid midfielder has formed a strong midfield partnership with Barcelona's Ivan Rakitic but Lovren feels that Modric's ability is under-rated.
"It is a real pleasure to play with Luka Modric, who is one of the best players in the world right now," said the Liverpool defender.
"Modric would probably be getting more attention than he is right now if he was a German or Spanish player. He would maybe even be a Ballon d’Or winner.
"Because we are a smaller country, he does get less attention than he deserves. But we are all football lovers and we know Modric is an incredible player. He is one of the best in the world right now," he said.
No Croatian has ever won the annual award for the world's best player although Davor Suker finished second in 1998, the year Croatia reached the semi-finals of the World Cup.
With Croatia already assured of a place in the last 16, coach Zlatko Dalic has indicated he will field a largely second string side against Iceland on Tuesday as he looks to protect six players who have yellow cards against their name.
A second yellow would lead to a suspension and while Group D rivals Argentina and Nigeria will want Croatia to go all out for a win, Lovren says they have to think of their own needs.
"I fully understand Argentina’s concerns and their wish for Croatia to play a full team for the next game as well. But we must also think about the fact that we should not be playing the players who have yellow cards," said Lovren.
"That’s also our concern we need to keep in mind. The coach is the one who will make the final decision. All of us are ready.
"Our goal of course is to get all nine points and we do not think the win over Iceland will be easy. We have played them in the past and we know they are a team that needs to be respected," he said.
Lovren said that Croatia's reserve players had beaten the first-choice eleven twice in three in-house games.
Rakitic, Ante Rabic, Sime Vrsaljko, Mario Mandzukic, Marcelo Brozovic and Vedran Corluka are the six Croatian players who are one booking from suspension.
(Reporting by Simon Evans; Editing by Amlan Chakraborty)
