Eriksen has long been regarded as one of the brightest talents in European football and the Denmark international only has one more season to run on his Ajax contract.
The 21-year-old confirmed last week that he was uncertain about his long-term future at the Amsterdam ArenA as he had not received a 'detailed' offer of a contract extension.
Reports in the Dutch and English media have subsequently claimed that Liverpool are favourites to snap up Eriksen in a transfer worth around €20million (£16.9m).
Ajax technical director Overmars would not comment on the transfer rumours, but acknowledged that Liverpool have regularly had scouts watching their games.
"We have a list of scouts from foreign clubs who have visited us and Liverpool have been a frequent visitor," Overmars told De Telegraaf.
Eriksen has been repeatedly linked with a move to the Premier League, with Arsenal, Manchester United and Tottenham Hotspur among the other clubs to have a reported interest.
Meanwhile, speculation has also suggested that Shakhtar Donetsk's Henrikh Mkhitaryan and Newcastle United winger Hatem Ben Arfa are alternatives for Rodgers if the Liverpool manager fails to land Eriksen.