Vieira spent the 2025/26 campaign on loan at Hamburg, his second loan spell away from Arsenal in as many years.
The 25-year-old flourished as an attacking midfielder in the Bundesliga, producing 12 goal involvements in 29 appearances for a Hamburg side that finished 13th.
According to reports, the German giants hold a 20m (£17.2m) option to buy the Portuguese playmaker, and Florian Plettenberg has revealed they're "doing everything" behind the scenes to keep him.
Hamburg want to build their team around the Arsenal loanee, and Vieira is "open" to staying in Germany after a productive campaign.
An agreement must now be reached with the Gunners to sign the attacking midfielder permanently, with his contract at the Emirates expiring in June 2027.