In return, says the newspaper, Wright "agreed to help the agent sign up Barnsley players, and recommend that the club sign other players represented by the consortium". The report added that "he would also look out for players at other clubs who the firm could approach".
In a statement on Wednesday night, Barnsley said they were "aware of the allegations made by the Telegraph against Tommy Wright". It added: "The club have today suspended Tommy pending an internal investigation into these allegations."
QPR manager Jimmy Floyd Hasselbaink and Leeds owner Massimo Cellino have also been targeted by the Telegraph. Both individuals, as well as Wright, deny any wrongdoing.
QPR said: "The club are aware of the allegations made against QPR manager Jimmy Floyd Hasselbaink. First and foremost, the club take very seriously any alleged breach of the rules. With this in mind, the club can confirm there will be a thorough internal investigation regarding this matter. However, we have every confidence in our manager and the robust systems and processes the club have in place."
In his own statement, Hasselbaink said he has been offered "a fee to make a speech in Singapore". He added: "I do not see anything unusual in being offered to be paid to make a speech. I did not make any promises in return. I did not ask QPR to purchase any of the players. I deny any accusations of wrongdoing."
Earlier in the day there were calls from Westminster for action, with minister for sport Tracey Crouch demanding that "all the evidence presented to them must be investigated".
On Wednesday night a joint statement issued by the FA, the Premier League and the Football League said: "English football takes the governance of the game extremely seriously with integrity being of paramount importance.
"Any substantive allegations will be investigated with the full force of the rules at our disposal, which are wide-ranging and well-developed. In addition, should we find any evidence of criminality we would inform and seek the support of the appropriate statutory authorities."
FA chairman Greg Clarke, who earlier this week was central to the decision that saw Sam Allardyce lose his job as England manager, admitted the governing body lacked the power to root out financial impropriety.
He said: "We don't have judicial powers, so we can't go and get a court order and do things like that."