"I expect that (the ruling coalition) will agree on a candidate this week and I'd like to present (the candidate) to the president at the end of the week," he told reporters on Monday.
"The responsibility is primarily on that political party under the (coalition) agreement and we, together with the party and its leadership, are in the process of discussing and looking for a candidate or candidates," he said.
The position has been vacant since the resignation of Milda Vainiutė on March 9 amid criticism from the president.
Skvernelis last month proposed Giedrius Danelius, a lawyer, as a candidate for the post, but President Dalia Grybauskaitė refused to appoint him.
On 27 May Lithuanian government has allowed renewing more flights to Germany and the Netherlands .