If the claim is accurate, the government wants to know at what level ISIS knew of or sanctioned the attempted attack.
Overnight, a video of Sunday's shootout was posted online, showing a compilation of news stories about the Garland shootings, but experts don't think it was put up by ISIS.
"It looks like that some supporters of these two attackers have pieced together various materials," said retired FBI agent Buck Revell.
Revell heads up the Revell Group and is chairman of the Middle East Media Research Institute.
"If it had been done in their normal fashion, it would have been much more professional and been done up front, with the Shaheed actually doing a video with their last testament," said Revell.
Nadir Soofi and Elton Simpson are the two suspects who are accused of carrying out Sunday's attack at the Garland Culwell Center. There, a Muhammad cartoon contest was taking place, sponsored by the American Freedom Defense Initiative.
"These people did have a link into people who have been identified as involved with ISIS," said Revell.
Revell says that link is a man known as Miski, or Muhammad Hassan -- an ISIS recruiter and U.S. fugitive since 2009.
Revell says Miski had been in contact with Simpson in the months before Sunday's attack.
The FBI had been monitoring Simpson's online activity since March 10, but he was not under surveillance, not believing he was an imminent threat.
"There were a number of posts that were certainly indicative of there was a...an attack being planned and it was being exalted by supporters," said Revell.
Police vaguely acknowledged that in a Monday news conference.
"Had there been chatter over a month or so from time to time, yes, but no specific threat," Officer Joe Harn with the Garland Police Department said Wednesday.
Until a tweet from an account traced to Simpson with the hashtag #TexasAttack appeared minutes before Sunday's shooting.
In a new warning supposedly from ISIS, the group claims 71 militants in 15 states.
"They are here," said Revell. "Of course they are here. Of course that doesn't mean they've come in; that means that means that they have been the enemy within. They have been essentially recruited, they self-radicalized or they've been radicalized and they have become…a fact that we have to deal with."