Hodgson's reputation has soared since guiding the club to their highest top-flight finish and the final of the Europa League, while operating on a modest budget.
The 62-year-old has been linked with a move to Liverpool and has even been mentioned as Fabio Capello's most likely successor when the England coach steps down.
While some of Fulham's over-achieving players may also now attract interest from rival clubs, Hangeland insists their newly-crowned Manager of the Year remains the key asset.
"Roy's the main reason we reached the Europa League final, it's as simple as that," said the Norway defender.
"We have a good group of players who have worked hard but it's all masterminded by him. He's done really well.
"I don't know what will happen now but I hope he stays because he's been so important to the success we've had over the last two years.
"Probably the most important thing for us over the summer is to make sure that he stays."
Former England left-back Paul Konchesky is one of several players who has seen his career revived by Hodgson's arrival.
"Roy is a big factor for the players and for the club," said Konchesky. "He's done well for the two and a half years he's been here and hopefully we can keep him and kick on again next year.
"The work he puts us through on the training ground and the squad he's built make him stand out.
"Whoever plays, they know exactly what they're doing. We've stuck together and that comes from the manager and the staff."
Hodgson's first spell in the Premier League ended under a cloud 12 years ago when he was sacked by Blackburn and only now is his nomadic and illustrious career receiving the recognition it deserves at home.
Under his expert guidance, Bobby Zamora has blossomed into one of the nation's form strikers who was on the verge of England recognition only for an Achilles injury to intervene.
"Roy has been absolutely magnificent and deserves all the praise he's been getting this season," said Zamora.
"If you ask any team this season they'll tell you how hard we are to beat.
"That comes from the gaffer - his organisation and willingness to work."
Wales midfielder Simon Davies, who fired the equaliser in last night's 2-1 extra-time defeat by Atletico Madrid, is confident Hodgson will stay.
"I wouldn't be surprised if he has offers on the table but he said he wants to continue with the job," he said. "I know he really likes Fulham and he's been a top manager since he's been here."