The Gunners were linked with a move to the Frenchman earlier this summer, before they strengthened their backline with the signing of Jurrien Timber from Ajax.
Arsenal paid £34m to secure Timber's services, and he made a positive start to his Arsenal career, putting in an impressive performance in Community Shield win over Manchester City earlier this month.
Timber subsequently kept his place in the side for Arsenal's Premier League opener against Nottingham Forest, but he was forced off in the second half with an injury issue.
Scans have since revealed that Timber sustained an anterior cruciate ligament injury and now faces a lengthy spell on the sidelines.
With Arsenal's defensive options weakened by Timber's absence, Mikel Arteta refused to rule out the possibility of signing another defender.
A recent report claimed that the Gunners could revive their interest in Simakan, who is under contract until the summer of 2027.
In addition to Simakan, Dani Olmo and Benjamin Sesko have also been linked with a move away from Leipzig, but Rose has laughed off the transfer speculation during a press conference ahead of Saturday's Bundesliga opener against Bayer Leverkusen.
As quoted by MDR, Rose told reporters: "I think Dani [Olmo] feels super comfortable with his role here at the moment.
"Nothing is impossible in this business, but I don't hope that anyone thinks there's a door open. I could say now, only about my... but I'm not saying that.
"Simakan to Arsenal, Olmo to Manchester City, I think Sesko is already dissatisfied and wants to go to Inter Milan!
"At some point it's good to, what should the people outside believe and what not? I need a team to be able to play football. If we remain ambitious, I also need good players."
RB Leipzig are reluctant to sanction any more departures, having already seen Josko Gvardiol, Dominik Szoboszlai and Christopher Nkunku complete moves to the Premier League this summer.
Simakan, who joined Leipzig from Strasbourg in 2021, has made 79 competitive appearances during his time with the German club.