Ross defected from the BBC in 2010 and was shortly confirmed to front a star-studded programme on his new channel later this year.
Although an airdate has not yet been set, ITV bosses revealed that they were considering scheduling Ross's show for Friday evenings, potentially putting it in direct competition with Carr's Chatty Man on Channel 4.
"I'm intrigued to see whether he's going to be a bit naughty," Carr told The Sun's Buzz magazine. "But I don't want him to be too good. I love Jonathan - but I don't want him showing me up."
Carr recently landed a £4m deal to host four more series of Chatty Man.
"People love coming on his show and we get some top-flight guests," a Channel 4 spokesperson said. "We've tied him down for two more years to stop anyone else getting him."