It has been reported that Lviv want to bring the 22-year-old winger back to Ukraine on a loan deal this summer if manager Neil Lennon sanctions a deal.
Oleksandriya are also interested in the Ukraine international, but the youngster will only return to his boyhood club if Lennon decides to let him leave for this season, according to the report.
Shved has been on the books of Celtic since January 2019 when he joined from from Lviv for a transfer fee reported by The Scottish Sun to be worth £1.75 million.
The winger spent the second half of the 2018-19 campaign on loan at the Ukrainian club before returning to the Hoops in the summer of 2019.
Shved struggled to make an impact at Celtic this past season, but he is a very talented and promising young winger who can be a success at the Glasgow giants.
Perhaps the 22-year-old should stick it out at Celtic Park for the first half of next season and then take it from there.