According to the dailymail.co.uk yesterday, Beevers is one of a number of players that the Merseyside club have got their eye on for purchase in the forthcoming January transfer window.
The 18 year-old centre-back has played only a handful of first team games but has received praise from boss Brian Laws this season and is regarded as a hot prospect for the future.
Wednesday were linked with Everton reserve goalkeeper Iain Turner in the summer following the players' successful loan spell at Hillsborough last season, however a swap deal involving these two players is unlikely as Laws has given his backing to current 1st choice keeper Lee Grant and if any bid for Beevers were to come to fruition the club are likely to prefer a cash bid rather than a swap deal.