Borini joined the Black Cats on loan from Liverpool last summer and has impressed Poyet, who is eager to make an offer for the Italian forward in the summer.
"Fabio has become a hero, a legend, which is great," Poyet told reporters. "He has really got into the club and the fans. He lives football, he's a top professional, he's always on time, he's always trying to be better in training. He's that type of person, he's always looking after what he's eating or what he's not eating.
"I don't know if it will be possible to sign him, it's out of our hands but I can tell you that we like him a lot and we will try. People will say the price is going up.
"I'm not going to lie, he's an important player, he's been great."
Brendan Rodgers made Borini his first signing at Liverpool in 2012.