Reports suggested that Ronaldo - who was not present at the ceremony - shunned the event having missed out on the honour, with his agent Jorge Mendes saying it was "ridiculous and shameful" that the former Real Madrid forward had not won.
However, following his team Croatia's 1-1 draw against Portugal on Thursday, Modric said Ronaldo had contacted him privately to congratulate him.
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Modric said: "Cristiano sent me a message, congratulated me and told me he is happy for me and I deserved it."
He added: "I have a good relationship with Cristiano Ronaldo and we'll have good relationship in the future too.
"Individual awards are important but I am not obsessed with them."
Modric, who led Croatia to the World Cup final this summer while Ronaldo's Portugal crashed out in the group stage of the tournament, will also compete against Ronaldo and Liverpool's Mo Salah for FIFA's The Best Men's Player of the Year award on September 24.
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