"The president has started meetings with the ministerial candidates. She will personally meet with every candidate," Daiva Ulbinaite told reporters.
Grybauskaite's key requirements for the candidates are competence and transparency, she said.
"In order to assess the reliability of the candidates and prevent corruption, all candidates will be screened as provided for by the Law on Corruption Prevention," the spokeswoman said.
The president will comment on the proposed candidatures only after she has met with all the nominees and after all of them have been screened for transparency, she added.
Skvernelis unveiled the line-up of his Cabinet, which will be made up of 14 ministers, earlier in the day.
Grybauskaitė has already met with Kęstutis Navickas, the candidate to become the environment minister, and is also scheduled to meet with Jurgita Petrauskienė, the candidate for education and science minister, Liana Ruokytė-Jonsson, for culture minister, and Rokas Masiulis, for transport minister.