Bennett has undergone surgery to mend damaged knee ligaments and is expected to be out for several months.
And Norwich manager Chris Hughton has enquired about Troisi, an Australia international who was once on Newcastle's books.
"I think the link is maybe there because of the Newcastle connection," said Hughton.
"What you tend to find is that in the process of doing the work we do behind the scenes to identify players there will always be lots of names that are thrown in and as soon as you ask questions about somebody that can find its way into the public.
"He is just one of numerous names that we have asked about. That is where we are on that one.
"We have lost Elliott for a good period and it is something we would like to do in that area before the window closes. If we do, fine, if not, then I wouldn't be too concerned but what we will do is keep going right through until the window closes."
Hughton is also chasing other, unnamed targets and - speaking at a press conference ahead of the weekend game against Southampton - said he expects to be in the market for new players right up until Monday's deadline.
One of City's summer signings, Gary Hooper, is yet to appear for the club after suffering a shin injury in pre-season.
The striker will resume light training this week and is expected to be available after September's international break.