Premier Sports Management International Limited has lodged an action at Dundee Sheriff Court claiming the Tannadice side had agreed to pay 10% of any future transfer fee when Russell agreed a three-year deal with the club in 2011.
The player, 23, was subsequently sold last June to English Championship side Derby County, for whom he has since played 20 times.
Premier Sports Management claims contracts it had with Russell entitle it to a 10% cut of the fee. Ten per cent was also to be paid to Russell, whose contract stated he was to be paid £1000 a week initially, rising to £2100 a week depending on appearances.
Documents lodged at Dundee Sheriff Court by the agency claim it was contracted as Russell's representative - and that the fee was to be paid within 30 days of any transfer. The firm is claiming the full £75,000 fee, plus 8% interest from the date it became due last summer.
However, United refuted the claims, stating Premier Sports Management did not have a contract with the club and that in any event the firm was not officially Russell's representative.
Lawyers for United state: "For anyone not a solicitor to represent a player in any matter related to his contract they must be a licensed players' agent and must submit a copy of any representation agreement."
Lawyers for Premier Sports Management asked for a further hearing and Sheriff George Way fixed hearings in March and April.