Cooper, 29, has featured in the Gulls' recent friendly wins over Yeovil and Salisbury with Knill and his staff monitoring him closely.
Despite two impressive performances from the former Bournemouth man, United are struggling to make the necessary funds available for his signature.
"I've spoken to his agent," Knill told the club's official website. "He's a very good footballer and it will all come down to finances.
"He is one of those who could play various positions but, predominantly, I'm looking for a centre-half and he gives us a lot more in possession because you can build through him.
"Shaun is talented on the ball and doesn't panic, so I really like that part. I'll speak to his agent and see where we are at."