Cardozo is also being tracked by Russian clubs Lokomotiv Moscow and Rubin Kazan, though The Foxes are believed to be leading the chase for the Paraguayan forward.
His agent, Pedro Aldave, has said that the striker will report for pre-season training as usual with Benfica, but admits that he could still be on the move, and suggests that England is a likely destination.
"Cardozo is quiet, he has a contract and feels good in the club. Something better may come about, otherwise there is England? Let's see."
The experienced striker joined Benfica in 2007 for around €9 million from Argentinian side Newell's Old Boys and has gone on to score 172 goals in 293 appearances for the Portuguese giants.
He only made 15 appearances in the league last season but still managed to score seven times and is now ready to experience a new challenge before his career comes to an end.
Leicester will need goals to stay in the Premier League and if Cardozo can transfer his Primeira Liga form to England, he will certainly score plenty.