"I have no confidence because I agree with the arguments that have been expressed by Stasys Jakeliunas," he told reporters.
Jakeliunas, a member of the ruling Lithuanian Farmers and Greens Union (LFGU), chairs the parliamentary Committee on Budget and Finance (CBF).
On Tuesday, the Seimas will debate a resolution, put forward by the ruling bloc, that calls for expressing no-confidence in Vasiliauskas.
The opposition tabled an alternative draft resolution to express confidence in the central bank governor, but the parliament did not agree to put it to a debate.
Skvernelis told reporters he did not know yet if he would take part in the vote on the no-confidence resolution, saying this would depend on his agenda.
The no-confidence resolution calls on Vasiliauskas to resign for "undermining the reputation of the Seimas" and "discrediting the Bank of Lithuania". If governor refuses to step down, President Dalia Grybauskaite is urged to begin the procedure of sacking him.
Last week, the opposition described the "assault" on Vasiliauskas as an element of the election fight and a conflict of interest.
Vasiliauskas is currently serving his second term as chairman of the Bank of Lithuania's board, the post he took up in April 2011.
The central bank governor is appointed by the parliament on the president's recommendation.