Poland's ruling Law and Justice party, led by Jaroslaw Kaczynski, opposes Tusk's reappointment, accusing the former Polish prime minister of interfering in domestic political affairs,
Diplomats say, however, that Tusk may be re-elected for another term of two and a half years despite Poland's opposition as he has strong backing from other European countries, including Germany.
Warsaw proposes that Tusk be replaced by Jacek Saryusz-Wolski, a member of the European Parliament, but diplomats say that he stands no chance of getting the job and that Poland will lose the post if the incumbent is not re-elected.
Grybauskaitė supports this view, saying that the post of European Council head is not assigned to one or another country and that Saryusz-Wolski is not a challenger to Tusk.
"I'll try not to speak about the so-called challenger, because he's not a challenger; I'll speak about the principles. Incumbent and former heads of state are elected as European Council presidents. Second, this post is not assigned to one or another country and it is not hereditary," the Lithuanian president said on LRT Radio.
"I'm saying purely theoretically that if Mr. Tusk happens not to be elected, Poland doesn't own this post. With all this in mind, I'd like to say that I think that Mr. Tusk will be re-elected," she said.
"Without doubt, we support Mr. Tusk. In two and a half years, he has proven to be capable of a rather strong stance on the issues that concern us," Grybauskaitė told journalists in Brussels on Thursday before the European Union's (EU) summit.
During their two-day summit, EU leaders are also expected to discuss the bloc's future following Britain's withdrawal. Germany and France favor a future multi-speed Europe with different countries integrating at different speeds in certain areas. The Lithuanian government does not rule out such an idea, but it is cautious about a possible integration in the areas of tax and defense.