Reports in England claim the Gunners are set to make a £21m offer for Goretzka, who has one year remaining on his contract at the Bundesliga club.
Goretzka has been used as a rotational option in Joachim Low's national set-up, but whilst impressing for his nation, Schalke's man - according to a report published by Four Four Two - has supposedly turned to his national boss in search of some invaluable guidance surrounding his club career in order to push on to the next level.
Speaking after his player, Low confirmed Goretzka's next move had been on the agenda at a pre-tournament chat and he observed a player "carefully planning his next career steps".
Loew agreed that Goretzka had performed impressively in the tournament.
"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.
"He has delivered in both matches and, given his youth, he is already quite a personality in this team", he said.
"He has done very well here and is intelligent enough to take the right steps [for his future]".
The Schalke midfielder scored in his country's opening 3-2 win over Australia in Group B, then put in a strong display in Thursday's 1-1 draw with Chile. "The travel time is something that needs to be considered, we travelled late at night from Kazan and travelling is always taxing and demanding", he said.