The Blic daily reports that the draft resolution, proposed by Serbia and expected to be on the General Assembly's agenda on 9 September, will not be withdrawn, but the document could be considerably changed by amendments on which all 27 EU members have agreed.
Citing sources from Brussels, the Serbian media report that the modified resolution would be without a statement that unilateral secession is an unacceptable model for solving problems.
Instead of that, the planned resolution would call on Pristina and Belgrade to resort to talks on all outstanding issues.
The talks are to be conducted under the auspices of the European bloc instead of the UN.
The Danas daily reports that Serbian leaders conceded to such formulations.
The document, proposed by the EU, would be presented to Tadic at his talks with Ashton on Tuesday evening.
The International Court of Justice has recently ruled that Kosovo's declaration of independence from Serbia in 2008 did not violate international law.
So far, 71 countries, including 22 EU members, have recognised this youngest European country.