The out-of-contract defender is expected to say his farewells at Turf Moor after spending more than six years at the club.
The ex-Brentford centre back will become a free agent after making just short of 200 league appearances for the Clarets.
He earned his first cap for the Three Lions against the Azzurri at Wembley Stadium as Lorenzo Insigne's penalty cancelled out Jamie Vardy's first half finish in a 1-1 draw.
Tarkowski's last appearance for his country came in September 2018 as he played an hour of the 1-0 victory over Switzerland at Leicester City's King Power Stadium.
However, with Gareth Southgate due to name his squad for UEFA Nations League games against Hungary (x2), Germany and European champions Italy in the summer, Tarkowski was keen to advertise his availability.
"That's how it goes when you get to the top end of the game, unfortunately for me," said Tarkowski, on being overlooked. "I've not given up on that ambition and hope of playing for England again one day and we'll see what the future holds. I still have the ambition to be there so we'll see what happens.
"I think every player wants to be a part of a World Cup so that hope's not gone. I've just got to perform to the level that I know I can do and then we'll see what happens.
"I've not given up on it, that's for sure. I've not retired from international football, just in case anyone was wondering! The ambition is still there, I'm still young enough, I feel like I've got something to give, so we'll see what the future holds."