The Spanish champions made an approach to sign the 18-year-old for next season with a view to integrating him into the first team within the next three years, according to his agent.
Tillman, who signed for a €500,000 fee from Greuther Furth in 2015, has reportedly attracted the attention of Real Madrid in the past year following a string of impressive displays in the UEFA Youth League and with the Germany Under-18 side.
Agent Christian Rossner has confirmed that Barca made an offer but that Bayern president Uli Hoeness personally intervened in order to keep the highly-rated forward at the Allianz Arena.
"There was a tangible offer from Barcelona," Rossner told Sport Bild. "They've observed him for months and they wanted to sign him for the new season.
"Barca's plan was to let him train with the first team and give him match practice in the second team. In two or three years he would have become a full part of the first team.
"Bayern president Hoeness vetoed it. They are confident Timothy can become a first-team player."
Tillman, who has played as a winger and an advanced playmaker, has represented Germany throughout his youth career but would also be eligible to play for the United States senior side.
He was taken on Bayern's pre-season tour of the USA last year and was included in the Champions League squad, although he is yet to make an appearance under Carlo Ancelotti.