The Bavarians have signed Mario Gotze and Robert Lewandowski from BVB in the last two summers and are rumoured to want to pay the 25-year-old's buyout clause next summer, believed to be worth €25 million (£19.8m).
Reus, whose contract with Dortmund runs until the summer of 2016, has been linked with a move to Manchester United, Manchester City and Liverpool in recent months.
But Gotze admitted on Sunday that he was keen to see his old team-mate join him at the Allianz Arena and Rummenigge has now confirmed the Bundesliga champions will make a decision on whether to launch a bid.
"To be honest, we'll discuss the matter internally and calmly. Then we will come to a decision," he told Kicker.
"At the end of the day, the player has to decide too. His release clause is well known. There's nothing more to say."
Dortmund have reacted angrily to Bayern's interest in yet another of their stars, with CEO Hans-Joachim Watzke speaking out against the Bundesliga champions several times for what he deemed to be a public courting of the player.
Bayern were in the race to sign Reus from Borussia Monchengladbach back in 2012 but were pipped to the post by their rivals.
Reus has one goal and two assists from his three Bundesliga appearances so far this season.