The envoys of European Union member states will seek a joint resolution, which could still be amended, in Brussels on Thursday with the aim of adopting it at a meeting of foreign ministers of the bloc on Monday, Reuters said.
"In the light of Turkey's ongoing and new illegal exploration activities, the EU decides to suspend negotiations on the overall air transport agreement and agrees not to hold further high-level dialogue meetings at this time," the draft said.
"The council endorses the European Commission's proposal to reduce pre-accession assistance to Turkey in 2020 and calls on the EIB to reconsider Turkey's lending activities, particularly with respect to sovereign-backed lending," the draft adds.
The draft also states that the EU will be prepared to apply further restrictive measures against Turkey if it continues to excavate.
We are trying to calibrate it carefully because we need Turkish cooperation in immigration, NATO and counterterrorism, "said an EU diplomat involved in the draft text of the statement.
"Some member states depend on Turkey for energy transfers, so we have to tread carefully, do not expect any large-scale economic sanctions," he said.
Diplomats said Nicosia was urging the use of tougher language in drafting sanctions.
The EU has frozen Turkey's long-stalled accession talks as well as negotiations to strengthen their customs union, accusing Erdogan of gross human rights abuses.