It is understood that Belgium international defender Lombaerts, who was signed by Dick Advocaat for Zenit in 2007, would cost a fee in the region of £5m.
Dutch forward Lens, meanwhile, has 29 caps for the Netherlands and could fetch up to £8.5m
Sky sources understand Sunderland would have no problem paying those fees for the players but they are just two of a number of signings manager Advocaat is trying to make.
Lombaerts, 30, began his career at Club Brugge before a three-year spell with Gent, and he has 35 caps for Belgium.
Lens, 27, is an AZ Alkmaar youth graduate who moved to PSV Eindhoven in 2010 and scored 34 goals in 96 Eredivisie appearances. He joined Kiev in 2013.
On Wednesday, Sunderland confirmed the signing of Liverpool defender Sebastien Coates on a four-year deal after his successful season on loan last term.
Sunderland also confirmed on Thursday that captain Lee Cattermole has signed a new five-year deal.