An unnamed top-flight club contacted the Blades hierarchy about Adams earlier this week, but they have turned down their advances.
Manager Chris Wilder has admitted that there has been interest in former Ilkeston forward Adams and Dominic Calvert-Lewin, but says that he wants to keep the pair in an ideal world, while being pragmatic enough to accept that a big-money offer could force the Blades’ hands.
Adams is also being monitored by Championship pair Huddersfield Town and Wigan Athletic.
Hull City are battling it out with Wolves and Blackburn Rovers to sign released Manchester United attacker Nick Powell, 22.
Powell made just nine appearances for the Red Devils after joining from Crewe in 2012 and had a loan spell at Hull in the second half of last term.
Hull have also been linked with West Brom winger Callum McManaman, Tottenham midfielder Ryan Mason and Chelsea defender Papy Djilobodji.
On the forward front, Wales sensation Hal Robson Kanu, available on a free transfer, has been mentioned as a target along with Augsburg forward Raul Bobadilla.
Middlesbrough, set to sign ex-Manchester United and Barcelona keeper Victor Valdes today, are also in the hunt for Fiorentina striker Khouma Babacar, according to reports in Italy.
Babacar’s agent is flying out to England amid reports of Crystal Palace and Boro interest.
The pacy 23-year-old Senegalese centre-forward managed seven goals in 24 competitive appearances last term.
Bradford City manager Stuart McCall has admitted there is interest in re-signing wingman Kyel Reid, although the club do have other more pressing priorities with the Bantams fairly well stocked on the winger front.
Reid featured 40 times on loan last term.
Meanwhile, Bradford have coolled talk of interest in Leeds United striker Lee Erwin, who played under McCall at Motherwell.
City are looking at two a German and a Polish striker in training and they could feature in Saturday’s friendly at Guiseley.