"I have a good opinion of him, because he is a professional who has worked for practically all of his career at the Finance Ministry, including the position of deputy minister," Grybauskaite said at her annual news conference on Thursday.
"We can see that the changeover to the euro was smooth, practically the smoothest of all the 19 nations," the president said.
"Thus, at least I personally see no reasons why I could not or should not nominate him for a second term," she said.
Vasiliauskas' current term of office expires in April. He stepped in as the governor of the central bank on Apr. 16, 2011.
In the spring of 2009, Vasiliauskas led Grybauskaite's election campaign.
The governor of the central bank of Lithuania is appointed for a five-year tenure. The number of terms of office is not limited.