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The Fulham left wing-back spent the 2022-23 campaign on loan at Oakwell and his deal with the London club expires shortly.
Barnsley had originally been interested in France under-20 international at the end of the winter window of 2022, but they had to wait until last summer to strike a deal.
He said: “I knew last season (about Barnsley in 2021-22) as in January, normally I would have come. It was at the end of the window and Khaled (El-Ahmed), the CEO, contacted my agent, but finally it did not work out.
“So I came in the summer and knew a little bit about Barnsley. It was a club that I had in mind after that (winter).
“After one year and now it is the summer, I am a free agent, so we are going to have a discussion with the board and my agent, so we will see.
“It is possible, but it depends and all the discussions will be in the summer.”
Larkeche made 23 appearances in all competitions for the Reds, with that total including just five starts at league level.
But despite struggling for starts in front of Nicky Cadden, the Parisian still proved himself to be an important squad member with his attitude and conduct earning praise from Michael Duff.
On his time in South Yorkshire, Larkeche commented: “It was basically my first loan and I am still developing.
“I am 20 years old and I am really happy that the manager gave me the opportunity and when he did, I tried to be present and here (ready) so if he needed to call upon me, I’d be ready. That’s the most important thing for me.
“It was a good first loan for me in knowing men’s football.
“It is a club where I made my professional debut and I will always remember it and Oakwell really well and I have got many good memories. Obviously, I wanted to play more, it’s normal. But I took positives.”