Clingan, a Northern Ireland international and one of very few Norwich players to have done themselves justice in the last season, was subject of a reported £3million bid from Fuham in January.
The club will likely be prepared to offload their star midfielder for less than that figure now, but the player himself would seem to have higher hopes than an outside chance of a Championship promotion push.
The People and the Sunday Mirror say he has rejected a switch to Chris Coleman's Coventry, and Clingan would be clever to wait until the transfer merry-go-round speeds up a little, with the likes of West Brom and Middlesbrough likely to lose key personnel and need proven second tier performers to replace them.
The major problem for Bryan Gunn with this approach is that it would not appear he can spend the revenue on a promise. The marquee signing of the summer, which is likely to be a striker, is going to cost money and will probably have to wait for a sale. But the likes of Liam Dickinson and Alan Lee are attracting interest from elsewhere, with Norwich's low initial bids unlikely to persuade anyone to wait around for them to increase.