Benitez has become frustrated by the protracted move for versatile Aston Villa midfielder Gareth Barry and is considering other options to strengthen his left flank.
But Quaresma may prove as difficult to sign as Barry after Porto put a prohibitive £31.7million price tag on the Portugal international.
Inter boss Jose Mourinho has been told to raise his £13.5m bid, while Liverpool are said to be willing to go no higher than £20m for the 24-year-old.