Sancho enjoyed a breakthrough campaign in 2018-19, contributing 13 goals and 19 assists in all competitions for the Bundesliga runners-up.
Reports suggest United's failure to qualify for the Champions League saw them end their pursuit of Sancho this summer, though interest remains in the 19-year-old.
But former Red Devils captain Rooney, who remains the club's all-time record goalscorer, has warned Sancho of the dangers of returning to the Premier League, instead believing his development will be aided by remaining on the continent.
"Dortmund is a great club with great fans, they trust their young players and you can see that in Sancho and the progress he has made in the last 12 months," he told Bild.
"Now Jadon has to ask himself whether he would get the playing time he gets in Dortmund when he moves to England, or would he just sit on the bench?
"Playing time is so important for a young player like Jadon, so if he gets the most playing time in Dortmund, he should stay there."
With a move for Sancho off the table, United instead moved for Swansea City winger Daniel James to bolster their attacking ranks as Ole Gunnar Solskjaer oversees his first summer transfer market as manager of the 20-time English champions.
Crystal Palace defender Aaron Wan-Bissaka has followed James through the entrance doors at Old Trafford with reports suggesting Harry Maguire could follow if the club meet Leicester City's asking price, though this figure seems to be rising every week.
Sancho, meanwhile, will be hopeful of combining with Dortmund new boys Thorgan Hazard and Julian Brandt next season following their arrivals from Borussia Monchengladbach and Bayer Leverkusen respectively.
Lucien Favre has also added Germany international defenders Nico Schulz and Mats Hummels to his squad as he looks to again challenge Bayern Munch for supremacy in Germany.