Adams (number 29) enjoyed a productive first full season at Bramall Lane
Leicester-born Adams arrived in Sheffield 18 months ago from non-league Ilkeston Town and burst on to the scene with two goals in the League Cup semi-final draw with Tottenham Hotspur at Bramall Lane.
Adams' double stunned Spurs
14 goals in 41 appearances last season further enhanced the youngster's reputation, and the Blades have no plans to lose him according to the Star.
Wigan's policy of signing young Football League talents served them well last season, with Will Grigg, Max Power and Sam Morsy all impressing en route to the League One title.
Grigg (left) was League One's top scorer last season
While Huddersfield are building an exciting side ahead of David Wagner's first full season in charge - with German defender Christopher Schindler arriving in a £1.8 million club-record deal this week - and would also be an attractive option for Adams.
Schindler (left) is the new man at Town
United, who released 10 players and put a further seven up for sale this summer, are also looking to add to their squad as they seek a return to the Championship after what will be six years away next summer.