The Northern Ireland international is available for a cut-price £3m after his current employers were relegated from the Premier League, with Leicester one of a host of clubs interested in signing the player.
Both Manchester City and Arsenal have been linked with moves in the past, whilst this is now the third transfer window in a row that the 'Foxes' have tried to bring the player to the club.
However, the demands of Evans' agent Colin Murdock are understood to be creating some trepidation among interested parties, with his demands of a £4m 'finders fee' (133% of the transfer fee) considered excessive in some quarters.
Both Arsenal and City are though to have been put off by the demands, which would come on top of a six-figure contract of at least three years in duration.