The club has seen what he is capable of in the Championship. That can give you an idea of what he'd be like at the next level, he's a good Championship player but doesn't have the ability to be a good Premier League player. If he really was good enough for the Premier League you'd think at the very least the newly promoted clubs like Palace, Hull and Cardiff would be interested knowing Saints want to sell, but they signed other targets. Instead Sharp was on loan in the Championship last season and this summer has attracted reported interest from Doncaster, Bournemouth and Sheff Weds.
Saints are looking to push on into the top half of the Premier League. To do that they need to sign Italian internationals like Osvaldo, not use Sharp. If Saints were happy to remain in the bottom half I'm sure Sharp would be reasonable cover, but Cortese has far more ambition than that and Sharp doesn't improve the current starting XI.