Bergwijn has emerged as a top target for the Bundesliga giants and has been heavily linked with a move to Manchester United in the past.
Bayern are understood to have turned to the PSV sensation after becoming frustrated at their attempts to lure Leroy Sane away from Manchester City.
And his agent, Fulco van Kooperen, has told Bayern do not need to rush as they weigh up a move.
“We have never, never said we are losing patience,” he said.
“Bayern are a great and huge club and it’s great they like Steven.
“They can take all the time they need.”
Despite that, Van Kooperen has also warned them they risk missing out if they drag their heels for too long.
He explained: “On the other side, it’s not a secret there are more clubs which like him.”
United are reported to still retain an interest while Tottenham, Ajax and Inter Milan are all keeping tabs on the 21-year-old.
He was previously asked specifically about a potential switch to Old Trafford and refused to rule out the possibility while admitting he is happy in Holland for now.
“Manchester United are a good club, without a doubt,” he said.
“But I am only 21 years old and in no hurry to leave PSV.
“When you join a new club, a better team, you automatically raise your level because of the level of the other players on the pitch.
“If something good comes up, I’ll be ready for it. Otherwise I’ll be happy to stay at PSV.”
Bergwijn scored 14 goals in 33 Eredivisie appearances last season and chipped in with another 12 assists.