Peat claimed United manager Craig Levein's inference that McCurry had cheated his side against Rangers at Ibrox earlier in the month had been "criminal".
In a controversial 3-1 defeat in Glasgow which ended any hopes the Taysiders' had of a UEFA Cup spot, the visitors were denied what seemed a clear penalty and had a goal chalked off for offside.
Despite McCurry going on to the SFA's website to admit that he had made a mistake with regards both incidents, United still made an official complaint to the SFA.
Peat ensured the matter would spill into the summer when he said at the weekend: "The general purposes committee will review the case and decide if Craig should be up before them.
"We don't tell them what to do but in my eyes using a word like that (cheated) is criminal."
United believe Peat may have prejudiced their hearing with his comment and the Tayside club issued a statement which read:
"Dundee United wish to record their deep concern that the SFA president has spoken out in his capacity as president of the SFA before the general purposes committee has decided if there is a case to answer.
"The use of the word "criminal" by the SFA president in Sunday's newspaper has meant, unfortunately, that we, as a club, will now have to seek legal advice on this matter."
A counter-statement from the SFA tried to play down the possible damage caused by Peat's remarks.
"There is no suggestion that the Scottish FA president is seeking to influence the work of the general purposes committee," it read.
"His remarks to the press were preceded by him saying just that.