West Brom top the list of clubs keen on the winger, 24, who is recovering from surgery to remove a blood clot.
Sinclair has three years left on his City contract.
But he has made just three starts since his £6.2million move from Swansea 12 months ago.
Baggies boss Steve Clarke pulled off a coup by landing Chelsea striker Romelu Lukaku on loan last term and is keen on bringing in a wideman.