But Hornets general manager Dell Demps, who has heard several trade overtures for the All-Star point guard, wants to meet with Paul and hear that from him, once lockout-related restrictions on front office contact with players are lifted, according to the report.
Demps declined to meet with reporters on Thursday, but has said that his top priority is to work on an extension.
Paul, who was working out with his current teammates on Thursday, described various reports about where he might be traded as "just rumors."
"You can't control it. It's always going to happen. It's part of the game," Paul said. "I'm just happy to be back with my team."
"I don't think about it, to tell you the truth," Paul said of the trade rumors. "I'm just ready to get out here and compete and hoop. This is what I do. I love it.
"I have a very tight circle and they know this whole lockout thing's been driving me nuts, so I'm just happy to get out on the court and compete. This is the way that I express myself, by playing basketball, so I can't wait to get out there."
The Times Picayune, citing two league sources, said that Paul has not demanded a trade to the Knicks.
In New York, Paul's friend and U.S. Olympic teammate, Carmelo Anthony, was asked if he did any recruiting on Paul's recent visit to New York, and if he will be part of such efforts going forward.
Anthony, speaking at the team's training facility in Greenburgh, N.Y., disavowed any such involvement.
"I'm not involved in that process. No way," Anthony said. That's a subject, a topic that I don't want to touch. I don't want to deal with that."
Anthony said he's leaving that decision up to Paul.
"We're very close friends. I'm pretty sure you guys saw him out here in New York, a lot," Anthony said. "Due to the players meeting and stuff like that, we hung out. But we never had any conversations about him coming to New York. That's something that I would leave up to him and him and his family and I'm staying away from that. "
Anthony also said he hopes Paul doesn't endure months of uncertainty, as he did with the Denver Nuggets before finally being traded to New York last season. The two did talk about that situation, he said.
"One thing I did tell him was, 'Just make the best decision for you and your family.' He responded back that he knew ... he saw what I went through last year," Anthony said. And I'm pretty sure there's a certain part of him that don't want to deal with that."
"I don't think the NBA needs that right now," he added. "We just want to focus on -- especially the Knicks -- we just want to focus on what we need to focus on. Getting better, getting everybody back in the gym and preparing for our first game in Christmas."
Paul, who has been the object of rampant trade talk because he can opt out of his contract after this season, joined Trevor Ariza and Quincy Pondexter at the team's suburban training center. They were working out with Paul's personal trainer because they cannot work with team staff until the new labor agreement is ratified.
Thursday was the first day NBA players were permitted to use team facilities for voluntary workouts since an agreement was reached to end the lockout.
"I've got to be the happiest person in the world right now just to be back in the gym, getting a chance to work out with a couple of my teammates," Paul said.
New Orleans has only five players under contract. Center Emeka Okafor, who is traveling in Thailand, is expected back as soon as this weekend. Jarrett Jack was expected to join the workouts on Friday.
Shooting guard Marco Belinelli, a restricted free agent who has a tender offer from the Hornets, plans to arrive by Monday.
Demps, who was allowed to start discussing the frameworks of deals with agents on Wednesday, must fill out the rest of the roster through a compressed free agency period. If the new labor deal is ratified as expected, the Hornets open camp Dec. 9.
The Hornets' regular season schedule is expected to begin in late December but has not been officially set.
Paul said he thinks the Hornets' priority should be to figure out whether free agent David West is willing to come back.
"That's like a brother to me," Paul said. "I've never played a season without him."
Information from The Associated Press and ESPNNewYork.com contributor Ian Begley was used in this report.