Gyökeres, 28, scored 21 goals across 55 appearances in all competitions last season as Arsenal won the Premier League title for the first time in 22 years.
Despite often playing a rotational role given Mikel Arteta's squad depth, he ended the campaign as one of the club's most important attacking contributors.
Atletico Madrid had been the most serious suitor, with reports suggesting the Spanish club were exploring the possibility of Gyökeres featuring as part of any deal for Julián Álvarez. Arsenal are not interested in that arrangement.
Romano has confirmed that any club approaching the Gunners about the Sweden international has been given the same answer — he is not available.
Arsenal's reluctance to sell is straightforward. Gyökeres offers a physical and direct profile that no other player in their squad replicates. With a contract running four more seasons, the club are under no financial pressure to move him on and consider his presence central to their plans for the title defence.
The Atlético approach is now understood to have been dropped following Arsenal's firm stance. A fee well above market value would be the only scenario in which the club's position could change, and there is no indication such an offer is forthcoming.
The situation illustrates a broader tension in Arsenal's summer. The club are reported to be pursuing Álvarez themselves, but have made clear that Gyökeres is not a makeweight in any deal and will not be used as currency. The two transfers are being treated entirely separately.
For Gyökeres, the backing of the club and the security of a long-term contract in a Champions League-challenging environment represents the best platform available to him at this stage of his career. His record of 21 goals in 55 appearances last season — many from the bench — suggests his output could be even higher with more consistent starts, which remains a possibility as the squad evolves.