The 17-year-old, who plays as an attacking midfielder, has garnered attention for his performances for Bremen's Under-17s side, having registered 18 goals and 21 assists last term.
Philipp has stepped up to the Under-19s side this season and has already got off to a flying start with two goals and four assists.
"I wouldn't want to rule out the interest in David from the English clubs," academy director Bjorn Schierenbeck told German media. "But I don't know exactly how firm it is. We would be very eager to continue working together with David.
"We have already held talks with him, and explained what his future career with Werder can look like."
Philipp's current contract with the Bundesliga side expires next summer.