An EU diplomat said Rome is "putting a knife on the member states throat" over migration even before the subject is discussed by heads of state.
"As one member reserved their position on the entire conclusions, no conclusions have been agreed at this stage".
Tsipras said any agreement with Germany would not have significant knock-on effects on Greece as only between 50 to 100 asylum seekers a month are crossing the country's northern border, according to the report.
France and several other European Union countries including Italy have reached an agreement on new wording for migration conclusions, a French diplomat said.
"I can not tell you that everything is settled", the French diplomat briefed reporters on the summit sidelines.
"It's a possibility I hope not to consider, but if we reach that point, on my behalf we will not have shared conclusions".
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German Chancellor Angela Merkel has described the talks as "make-or-break" for the union.
"Europe has many challenges but migration could end up determining Europe's destiny", she told German lawmakers.
"Either we manage it, so others in Africa believe that we are guided by values and believe in multilateralism, not unilateralism, or nobody will believe any longer in the system of values that has made us strong", she added.
The stakes for Merkel are particularly high, as her Interior Minister Horst Seehofer has given her an ultimatum to find a solution at Thursday and Friday's summit to curb new arrivals, failing which he would defy her and turn away migrants at the border.
"That's why it's so important".