Okaka, 20, started both of this season's Europa League matches between the clubs and scored the winner at the Stadio Olimpico in early November.
Hodgson was impressed enough to look into taking the Italy Under-20 international to Craven Cottage but faces competition from Portsmouth.
"Okaka is a possibility for us. We're looking into it and have shown an interest," said Hodgson.
"How far we go down that road will depend on other things like whether he wants to come on loan to England. The finances of the situation will also be important.
"Okaka has got quality and the fact it's a loan is also advantageous because he's a young player and largely untried.
"We're happy with our striking options but we would like to have some cover and someone who can put pressure on the guys we have.
"Okaka seems to be that type of player but a lot of water must pass under the bridge before he pulls on a Fulham shirt."