The France international has been strongly linked with a move away from St James' Park, with a return to his homeland mooted.
Cabaye has done little to curb the speculation by publicly welcoming links to Manchester United and Monaco.
Newcastle are, however, reluctant to part with players considered to be integral to their future.
Kinnear, who claims that he will have full control of transfer policy after agreeing a return to Tyneside, is adamant that Cabaye will not be among those the Magpies look to move on this summer.
He told the Evening Chronicle: "He will stay. We've got him under contract and we want to keep all of our top players here. We don't feel we have to sell our top stars.
"The only players we will move on are the ones that are coming up short. You can't have that at a massive football club like this.
"We will have to move them on. We can't have mediocre players at Newcastle United. But we won't be selling our best players."
Kinnear also insisted his shock appointment was approved by manager Alan Pardew, and the former Wimbledon boss is adamant they can form a good working relationship.
"Before I had a meeting with Mike (Ashley), Derek (Llambias) said he's informed Alan, and Alan said 'Great news - I'm delighted with that. At last I've got somebody who's a football guy'," Kinnear said.
"I have the utmost respect for him and I cannot see any problems between the two of us. I am not the type of guy who causes problems for the sake of it. I want the best for all of us."
The 66-year-old former Magpies manager met with the club's owner Mike Ashley on Sunday to sign the agreement and told Sky Sports News he will deal mainly with player recruitment and transfers, on which he will have the final say.
Kinnear managed Newcastle during the 2008/9 season but was forced to step aside after suffering a heart attack.
He told Sky Sports News: "It's absolutely done. I signed it with Mike today and that's taken care of. I think it is a very interesting role for myself and I don't think I could be at a better club doing it.
"I have been in discussions with Mike and once we clarified the situation and what my role would be, ie. in charge of transfers and looking at the strengths and weaknesses of the side that we have got and to help out Alan Pardew in every possible way that I can and use all the experience that I have from the game.
"I intend to meet Alan either tomorrow (Monday) or within the coming week to discuss the future and go through the team itself.
"Our target is that we have got to push ourselves up and try and do as well as we did a couple of seasons ago.
"I am as fit as a fiddle now. I am in the best physical shape that I have ever been and I have been waiting for the opportunity. I have had a great football career and I think I am ideal for this situation and I am looking forward to it."