Reports in Italy have linked Gabbiadini with a return to his former club but Pellegrino expects the 26-year-old to remain with the Saints as they continue their fight against relegation.
When asked if the Italy international was set to leave in January, Pellegrino said: "I don't think so.
"This morning I was talking with (vice-chairman of football) Les (Reed). Every day we are talking about some news in the market, if there is the possibility of some players trying to try to leave and some to bring in but nobody has told me anything about Manolo.
"He is an important player for us, obviously he is not playing too much at the moment but he is one of our main strikers and I want to keep him."