England international Sancho is rumoured to be a target for several Premier League sides and BVB's domestic rival Bayern Munich after another impressive Bundesliga season.
He has scored and assisted a combined 30 goals in the German top flight this season, placing him behind only RB Leipzig's Timo Werner in terms of overall goal involvements.
Delaney is confident Sancho will become one of the top-five players in the world but has suggested the 20 year-old is already feeling the heat to perform regularly at his highest level for club and country.
"He's clearly one of the biggest talents that I've played with," he told ESPN's Gab & Juls podcast. "With that talent comes a lot of pressure, and I think he slowly starts to feel that from the England national team and clubs surrounding him now.
"Up until this point, he's been a talent performing very well, performing better than what he is expected to do, but there was always going to be a next step, and that's going to be interesting, [the] next step in his career and his development.
"Only looking at his skills, he definitely has what it takes to become one of the five biggest players in the world. You see big talents go to waste, and I would say that he's already done enough to prove himself.
"He's 19 and he's got the most goal involvements in the league together with Timo Werner and [Robert] Lewandowski, which is amazing, but he should strive for more."
Sancho is not alone in being linked with a big-money move away from Signal Iduna Park, with prolific striker Erling Haaland also reportedly a target for numerous teams.
Haaland has scored 13 goals in 14 matches since joining Dortmund in January and Delaney can only see him getting better with time.
"I see a young man that does everything to improve," he said. "This guy is annoying sometimes because everything has to be on point with more training and eating better.
"I think he's definitely benefited from having people around him, especially his dad, that knows how things work in football. With Erling, I don't even have to mention the stats."
Delaney also heaped praise on American teenage midfielder Gio Reyna, who has featured 13 times from the bench in all competitions this season.
"With Gio as well, just coming in, an American kid, travelled a lot back and forth and still has his breakthrough to come," Delaney said.
"But he's a player you can expect more from him because in training he's on a level."