Hodgson has been watching the tough-tackling Northern Ireland midfielder but was told he was not for sale in the January transfer window.
Clingan, 25, a summer free transfer from Nottingham Forest, has been one of the few successes at Carrow Road this term.
New boss Bryan Gunn wanted to keep his stars for the relegation fight but could sell for the right price in the summer.
Clingan said: “I respect the decision to turn Fulham down. It’s my dream to play in the Premier League.
“But if Norwich aren’t happy to sell then they are entitled to say no.”