The 29-year-old, was an unused substitute during Holland's 3-0 demolition job over Italy, recently pledged his future to the Scottish champions, but this has done little to deter Lazio's interest.
"Vennegoor of Hesselink is a player we rate highly," admitted Biancoceleste president Claudio Lotito.
"We've been watching him closely for a while. His strength is a real force and he has a lot of European experience.
"He is a player who without question interests us but it depends what Celtic would ask for as a transfer fee.
"Beyond £5.5million is out of our reach."