Marxist scholar Eugene Genovese said yesterday that he would indeed "be happy to testify" on behalf of University of Dallas professor Melvin E. Bradford if he is nominated by President Reagan for the chairmanship of the National Endowment for the Humanities.

Bradford -- a conservative, a longtime Reagan supporter, a onetime Wallace supporter and a critic of Abraham Lincoln -- told a group of reporters Tuesday that Genovese would be willing to testify on his behalf at any confirmation hearing.

"He's a good scholar," said Genovese, a history professor at the University of Rochester, contacted by phone yesterday. "I don't agree with him, needless to say. But he's a very bright man. His work is tremendously stimulating."

Genovese, who has corresponded with Bradford on the issue of Lincoln, said he first read "attacks" on Bradford in a newspaper a month ago and found them "McCarthy-like. He was under attack because of his negative attitude on Lincoln." Bradford has criticized Lincoln for his interpretation of the Constitution and his handling of the Civil War.

Genovese said Bradford was being judged "not on his scholarship but on the nature of his political views." Genovese then called Bradford "to say that I hoped the story about his nomination was true. I expressed my concern about the attacks and told him that if I could be of help to let me know."

In other remarks to reporters Tuesday, Bradford harshly assailed the NEH, claiming that the agency had awarded some grants on the basis of politics, not scholarship. Bradford also said he would award more grants to conservatives.

"That's what I like about him," said Genovese. "He's outspoken."

A Reagan administration source characterized the now drawn-out process of choosing a nominee for the NEH post as "a political football. . . . The whole thing is such a tempest in a teapot. I just hope they announce somebody, anybody on Thursday and get it over with." There had been talk that a White House announcement of an NEH nominee would occur today, but that now looks doubtful.

Frank Madsen, an administrative aide for Sen. Orrin Hatch (R-Utah), one of 16 Republican senators who signed a letter of support for Bradford, said that Hatch had no reply to Bradford's criticisms of the NEH. Madsen said that Hatch's support of Bradford "was predicated upon what his colleagues said to him. Several approached him about Bradford." Hatch, said Madsen, "has never had a conversation with Bradford . It's not like he knows him personally."