Hamburg want to keep him but are unable to meet the 20 million euro purchase option agreed with Arsenal.
Vieira spoke to Bild at the end of the season and acknowledged he needs to weigh all the factors before a decision is made.
"Now I go on holiday with my family, to forget football for a while. That's important, not to think about it for a bit. We are in a transfer period. I have to be open, speak with my family, my advisers and Arsenal, and decide what the best option is."
He praised the Hamburg supporters warmly before addressing the question of his future directly.
"Whether I stay or leave, I will always be grateful to this club. They did everything for me. At the end of the day, the most important thing was that HSV stayed in the league. And I was part of that, which makes me very happy."
HSV head coach Merlin Polzin made no effort to hide his desire to keep the player.
"I know that he appreciates being able to express himself fully here with his qualities, and that it helps him how we play football."
Vieira returned the compliment, describing the 33-year-old coach in terms that went beyond professional appreciation.
"Merlin has helped me a lot. He always tries to make sure I can show the best version of myself. He is still young but has the mentality and the qualities to challenge the biggest clubs."
The obstacle is financial. HSV have already agreed a follow-up contract with Vieira in principle but cannot activate the 20 million euro clause, with Bild reporting their maximum budget sits in the high single-digit million range. Arsenal are unlikely to accept a figure significantly below the option agreed, and a second loan is not under consideration. With Vieira's contract in north London running until 2027, Arsenal will look to sell this summer to avoid losing him for nothing. Other clubs are expected to enter the picture if talks between HSV and Arsenal stall.
Vieira contributed 12 goal involvements across the Bundesliga season, registering direct returns against Bayern Munich, Borussia Dortmund, RB Leipzig and Stuttgart among others.