The Scotland international is a free agent after walking away from former club Sunderland following the expiration of his contract at the Stadium of Light.
Fletcher scored 23 Premier League goals in 94 league games for the Black Cats, yet he struggled to make any in-roads under Sam Allardyce last term and spent the second half of the season on loan at Marseille.
The 29-year-old still posseses ability and a recent report in the Daily Record claimed Premier League side Hull City are keen on his services along with Aston Villa and Scottish champions Celtic.
The Hoops are seemingly on the lookout for a new striker to partner last season’s top scorer Leigh Griffiths and the former Wolverhampton Wanderers man could be seen as a positive free agent addition.
Sky Bet previously had Celtic as favourites to sign him, as documented by HITC a fortnight ago, yet now their odds have drifted slightly to 11/8 while Sheffield Wednesday are the new frontrunners with odds of 4/5.
The Owls narrowly missed out on promption to the top-flight last season as they lost 1-0 in the Championship playoff final to Hull, yet there remains plenty of optimism around Hillsborough.
Carlos Carvalhal is being backed by wealthy owner Dejphon Chansiri and this season the club is expected to be in the mix for automatic promotion alongside the likes of Newcastle United and Norwich City.
Fletcher would provide something different to the likes of Gary Hooper and Fernando Forestieri, though any deal for the English-born Scot could see the club break their current wage structure.