Fletcher is a free agent at the moment, having recently been released by Premier League outfit Sunderland.
It has been reported by The Sun that Wednesday want to recruit the Scotland international striker this summer in order to boost their chances of winning promotion to the Premier League at the end of the 2016-17 campaign.
The former Wolverhampton Wanderers striker reportedly wants £40,000 a week as salary, and Wednesday have put their pursuit of him on hold until his wage demands come down.
Wednesday are not the only club interested in securing the services of Fletcher this summer, though.
Fletcher scored four goals and created eight chances in 16 Premier League appearances for Sunderland last season before joining Marseille on loan in the January transfer window.
The 29-year-old former Hibernian striker scored two goals and created 16 chances in 12 Ligue 1 matches for Marseille.