Jordan Rhodes spent last season on loan with the Canaries, hitting nine goals in 40 appearances to help fire the Norfolk club to the Championship title.
Speaking to The Pink Un, Norwich's Sporting Director Stuart Webber admitted Norwich "would love" to sign Rhodes on a permanent basis.But Webber conceded the club may have to look elsewhere to strengthen their attacking options.
He said: "First of all, we never had the option to buy him, in writing. We couldn't agree that last summer so we didn't have it. It was just a straight forward loan. So it's not like we've tried to renegotiate that, it never existed.
"It's a difficult one with Jordan because he did so well for us, on and off the pitch. When we talk in terms of the cultural architects within the group, which we've spent a lot of time developing, that's so important, that people get what we want to be."He was an unbelievable leader in that and people will never - unless you're in the building every day - appreciate what he gave to this club - in terms of other than the important goals he scored, which were there for all to see.
"So if there was a way we could bring him back that would be great but at the same time, he's 29, he's got two years left on his contract at Wednesday, their valuation of him last summer was outrageous and that will be pretty high again.
So it's a really difficult deal for us to do. We've got a really small budget and to go and spend a lot of that on a 29-year-old who has a pretty high salary, which is well documented, that would be tough - for someone who was a number two striker, in the end, in the Championship."
Scotland international Rhodes, whose uncle is Owls assistant manager Steve Agnew, largely provided back-up to 30-goal centre-forward Teemu Pukki. Twenty nine of his appearances came from off the bench.
Webber said: "We could be signing him and potentially another striker for the Premier League and then you're thinking, does it make economic sense?"So it's a tough one, a real tough one. We would love to bring Jordan back because of what he brings and we truly believe he would score goals in the Premier League. The goals are the same size and the thing with him is he knows how to score, he knows where to stand and somehow when the ball gets delivered he's always there."The way he supported Teemu and Dennis (Srbeny) was unbelievable but I think it's a long shot for us, if I'm honest - and it pains me to say that."