The forward only joined last summer from Deportivo La Coruna for £17million.
And while he has impressed in fleeting spells, the 28-year-old has failed to establish himself as a key player in north London.
Arsene Wenger has preferred Alexis Sanchez and Olivier Giroud up front, while 20-year-old Alex Iwobi has featured more at left-wing.
Lucas Perez has made 10 Premier League appearances in total for Arsenal
The Spaniard will consider moving on just one year after arriving in England
Perez has been restricted to appearances largely in cup competitions so far this season.
And according to the Daily Mail, the Spaniard will consider moving on just one year after arriving in England.
The former Deportivo star, who netted 17 La Liga goals last season, has earned just two Premier League starts for Arsenal.
Lucas Perez's only Premier League goal came at Bournemouth last month
Arsenal line-up predicted to face Bayern Munich
Mon, February 13, 2017
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Lucas Perez has been restricted to mainly starts in cup competitions for Arsenal
Perez has failed to play a full 90 minutes in the top flight, having scored just once as a substitute at Bournemouth.
Despite his five goals across the EFL Cup and Champions League, a future as an influential player for Arsenal appears unlikely.
He is part of Arsenal’s squad travelling to Germany to face Bayern Munich tomorrow night (7.45pm), but he is not expected to start the crunch tie, despite the Gunners’ injury problems.