The Gunners failed with an offer for the 23-year-old last summer, but Chief Emery is ready to try again.
Gbamin, who is wanted by a number of Premier League clubs, has moved into the ranks of Lens before switching to the German Mainz team.
But their £ 40 million purchase price would consume almost all of Emery's £ 45 million budget.
And Gbamin opened the door to a summer transfer away from the Bundesliga team.
The goal of Arsenal reported is eager to make "the next step" after 12 months from seeing a stuck move in the Premier League.
He told Goal and Spox: "Basically I feel ready for the next step and I can well imagine starting a new chapter.
"Through my results, I have made the clubs aware of myself, where I see good chances to go to this next phase of my personal and sporting development.
"At the moment I give 100% to Mainz and I am very satisfied with how much we have improved.
"What will happen after the season, we have to wait and see."
Arsenal came on loan to Denis Suarez from Barcelona in January, but the midfielder has yet to start a game.
And the 19-year-old summer signature, Matteo Guendouzi, continues to keep Mesut Ozil out of Emery's line-up.
Gbamin would prove to be a valuable resource for the Gunners as he can operate as a midfielder or midfielder.
"Obviously, the club's position initially frustrated me," he added.
"Anything else would not be normal, I would say, I thought it was possible to transfer, that's why I made it public, and it turned out different."
Emery led his team to a 2-1 victory against Huddersfield, at risk relegation, to John Smith's Stadium.
Arsenal's win means that they tie at Chelsea with 50 points, but remain in sixth place for goal difference.