The striker has not featured in manager Mark Hughes' squad since he sent a text on the eve of the recent 5-3 home defeat to Liverpool to say he was unavailable for selection.
Trinidad and Tobago international Jones was fined two weeks wages -- around £80,000 -- and left out of the squad for last weekend's 1-0 defeat at Crystal Palace, but has been training with the rest of the group this week.
Hughes said: "At the time, I was not happy with what happened. We have discussed a few things, and he knows the situation and the club's feelings on the issue.
"The club is aware of the player's feelings as well. He has trained correctly since. He has shown he wants to do things right and be professional, and he is available for selection.
"There has been no problem with the group. The group is a good group, and there would have been a reaction if Kenwyne had not applied himself and approached things in the right way.
"Nothing has happened with Kenwyne in terms of the transfer market. You never know how things might develop for the rest of the window, but at the moment we cannot afford to let him go out because that would weaken us."
Hughes also made it clear that Peter Crouch would not be allowed to join Queens Park Rangers this month, and said he was hopeful loan signing John Guidetti would be available at Stamford Bridge despite missing Friday training because of illness.
"We will have to wait and see how he is," he said. "Hopefully, it will be a 24-hour thing. I wanted to give him some game time and see whether he can show he can do the things we want him to and score goals for us."
Cardiff close on Jones transfer, with Peter Odemwingie offered as makeweight
The Bluebirds aren't too keen on the Nigerian, so are offering him as bait to secure the signing of Jones
Cardiff boss Ole Gunnar Solskjaer was last night trying to tie up a deal for Stoke striker Kenwyne Jones.
Solskjaer is ready to let Cardiff’s Peter Odemwingie go in the opposite direction in a surprise swap deal.
Cardiff are desperate to boost their fire power in their battle against relegation and it would represent a fresh start for Jones.
Mirror Sport revealed earlier this month that Jones refused to play against Liverpool and had been fined two weeks’ wages by Stoke for a breach of discipline.
Stoke boss Mark Hughes had been set to bring in Jones from the cold to face Chelsea on Sunday in the FA Cup.
But the potential swap deal shows that Stoke are clearly putting Premier League survival first.