Robin Van Persie
The Netherlands international was heavily linked with an Ibrox switch, but Warburton has explained why a deal will not happen.
"Out of our pay league I think is a fair comment," he told the Evening Times.
"He's an unbelievably talented player but absolutely nothing in it whatsoever. I'm bemused to hear some of the stories, including betting being suspended."
Kennedy was responding to questions about whether the Hoops had bid for the 27-year-old as reports had suggested. And while he did not confirm or deny the move, he did admit that he is on their radar.
"He is one that has been mentioned, but he's still an Aston Villa player. That is certainly the calibre of player we're looking at," he told BBC Sport.
Thompson also outlined how many more signings he would like to see before the window shuts.
"Kolo Toure will be good for them. He's experienced, he's calm, he's got a presence, but I think they would fancy that they could need one or two more," he told The Scottish Sun.
"Kolo is a great signing for Celtic. He has so much experience playing at the top level for Liverpool, Manchester City, and Arsenal," he told The Scottish Sun.
The midfielder has already represented England at four youth levels, and he has backed Warburton to help him to continue moving through the ranks.
"The manager can definitely help me. He is always speaking to you, helping you out," he told the Evening Times.
"He really is a gaffer that wants to help. That's what you need in a big team."
Finally, Warburton has explained to the Evening Times that summer signing Matt Crooks is now back running again after recovering from injury, and will be line to make his Light Blues debut in the near future.
"Matt was running on the grass [on Thursday] morning so hopefully he is two weeks away from joining the squad again. Obviously he will have to catch up with his fitness," he told the Evening Times.