Can, 28, is proving a problem for the manager and his teammates, and is now understood to be on the club's transfer list.
The Germany international has played 83 times for the German club since joining in a £22.5million move from Juventus in 2020.
According to Bild, Terzic's side are set to part ways with the player if they receive a suitable offer, with Can having two years remaining on his current contact.
They state his performances do not justify his behaviour off the pitch, but do know he is outspoken and self-confident in general.
It is believed the ex-Liverpool midfielder lectures his teammates and the boss himself, which has left all very 'irritated'.
The former Bayern Munich academy graduate is understood to have allegedly interrupted a team talk when previous manager Marco Rose was in charge.
Can is currently nursing a muscle injury having picked up a slight knock at the start of pre-season.
In 2021/22 he was plagued by similar problems which meant he missed a total of 17 competitive games.
The two-time Serie A winner with Juventus is understood to earn around £7.2m-a-year, which works out at £138,000-a-week.
Bild do go on to say that his wage demands could prove difficult in him finding a new club ahead of the upcoming season.
BVB may opt to leave the player out in the cold it is believed, should the German fail to leave before the end of the transfer window.
It is not the first time Can has annoyed his manager, having complained to Jurgen Klopp whilst at Liverpool.
"I already complained to Jurgen Klopp about the hard training in Liverpool! But the training here at Juventus is a bit tougher," Can told an interview with DAZN and Goal.com.
"We have to run even more, do more strength training. It was a big challenge for me at the beginning. But now my body has got used to it."
It remains to be seen where Can will be plying his trade next season, but his days seem to be numbered at Borussia Dortmund.