Goretzka currently plies his trade for Bundesliga side Schalke 04 but after a couple of below-par seasons with the Royal Blues, the lanky midfielder is considering his options.
The 22-year is hoping to find a club where the level of football will help him cement regular playing time under national team coach Joachim Low.
Gunners boss' Arsene Wenger is a known admirer of the box-to-box midfielder and after impressive displays in Die Mannschaft midfield at the Confederations Cup in Russia - a possible move away from Gelsenkirchen looks increasingly likely.
"As soon as the facts are there, I will be providing, then publicising what my decision is. But today there is no news to that effect," Goretzka said after scoring against Australia in the 3-2 win.
Low himself also commented on the rife speculation, claiming the pair had a private conversation before the pre-World Cup showpiece.
"Between the matches against Denmark and San Marino we had a long conversation about different possible scenarios because I just wanted to know what he was thinking, what kind of opportunities he envisaged," he told reporters.
"I certainly spoke my mind, but please bear with me if I don't share any details. It was a personal conversation and he said he would not focus on his future, he would focus on the Confederations Cup.
"To date, he has delivered. He played very well in both matches and, given his youth, he is already quite a personality in this team.
"It does seem to be clear that he is carefully planning his next career steps and therefore we are trying to ignore the whole issue surrounding his future club career. He is intelligent enough to come up with the right decision for his own career."
Goretzka scored eight goals and registered six assists in 41 games last season - helping Schalke to the Europa League quarter-finals and a tenth-place league finish.