The 23-year-old centre-half is currently being kept out of the Celtic first team by Cameron Carter-Vickers and Carl Starfelt, while the arrivals of Japanese defender Yuki Kobayashi and fellow countryman utility player Tomoki Iwata has enhanced competition in that part of the first team.
Welsh, who has also been linked with moves to Udinese in Serie A and French Ligue 1 outfit Toulouse, is a boyhood Celtic fan and has come through the youth academy. However, he has struggled for regular game-time under current manager Ange Postecoglou and now has to weigh up what is best for his career, with Owls manager Darren Moore looking to strengthen for a promotion push from Skybet League One, where they currently sit second in the table.
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Hide AdWelsh also has other admirers in England, while teams in Scotland are monitoring his situation.
