The Brazilian is on loan with the Championship side for the rest of the campaign having had his opportunities at Wolves limited.
Forest, who are ninth in the table and four points off the play-offs, have an option to buy Bonatini in the summer.
When asked if he wants to stay, Bonatini said: "Yes, of course.
“It is a really good team and they have very good conditions here.
“Even if we don’t achieve the play-offs and we are staying in the Championship next season, I would like to stay because I have found it really good.
“But of course I know that it is not just about me; I have a contract with Wolves. But I am enjoying being here.
“I think it depends how I finish the season here. Wolves are doing well, too.
“I don’t know. It’s something we’ll just have to wait until the summer.”
Bonatini has played four times for Martin O'Neill's side – all from the bench – and is yet to find the net.
He's keen for more minutes on the pitch to show what he can do.
“I wouldn’t say there is pressure. I am enjoying being here at this club,” he added. “They have given me the opportunity to play and to have some minutes.
“I am here to help them.
“I’m here to help them and to hopefully achieve the play-offs, then we will go hard to achieve our goal.
“The club is very good. My family is here as well, my parents like the city.
“I’m very happy to have joined the club in the transfer window.
“Hopefully we can achieve the play-offs and get to the Premier League; that’s one thing we really want to do.”