Morrison would welcome the chance of a reunion with his former Republic of Ireland manager Mick McCarthy - now in charge of the Wearsiders - who is believed to be interested in acquiring his services.
Morrison was Blues' club record signing when he moved from Crystal Palace in a £4.5 million deal in the summer of 2002.
But he has struggled to make an impact and was hampered by a severe shoulder problem during the second half of last season.
This season he has found himself behind Christophe Dugarry, Mikael Forssell and David Dunn, who at times has been played as the second striker, in the pecking order.
Morrison said: "I'm very frustrated at the moment. All I can do is carry on doing my best in training but it's hard to impress when you are not starting games.
"Strikers want to get on the field and show what we can do. We're hungry to play all the games and that's the way I am now. You can't make an impact when you get three minutes here and five minutes there.
"The manager says that I am in his plans but I am not enjoying sitting and watching others play football.
"There's been some talk about Sunderland. Mick McCarthy knows me and I know him. He's a great coach and I'd love to work with him again even if it was just for a month or two.
"I need to play matches, to get goals and I need to regain match fitness and, if I do, then there's something in it for Sunderland as well because they are going for promotion."
