The 22-year-old, who is heading to Russia with the Turkey national team next month, is understood to be valued at £35m by his club side.
Soyuncu's agent recently talked up a move to the Premier League, and the centre-back has now offered a big indication that a switch to the Emirates Stadium - despite a new manager being brought earlier this week - is on the cards.
"Arsenal are one of the most important clubs in England," he told reporters in his native Turkey. "I know they're interested in me, but there's nothing finalised yet about my transfer. After the national team camp we'll have talks."
Soyuncu was used 31 times by Freiburg in all competitions last season, including 25 times in the Bundesliga.