Barry only joined Everton for £27 million from Villarreal last July, and was seen as a marquee signing by the Toffees.
Stepping up to the Premier League is always a challenge, though, and the 23-year-old took a while to acclimatise, eventually scoring eight top-flight goals in his debut campaign.
Two of those came in an incredible 3-3 draw against Manchester City that effectively handed Arsenal the title, and now he could already leave the club.
According to The Times, Everton are looking to recoup the initial £27m they spent on him last summer after RB Leipzig submitted an "enquiry" for the France under-21 international.
David Moyes is keen to upgrade his forward line in their pursuit of Europe next season, with the same report revealing that a loan deal for Chelsea's Liam Delap has been explored.
Delap has struggled since joining Chelsea from Ipswich Town last summer, but did bag 12 goals in the season prior as the Tractor Boys suffered relegation to the Championship.