Manager Robbie Neilson confirmed that he will speak to the 26-year-old left-back, impressive in nine appearances since arriving at Tynecastle Park last month.
Kingsley signed a contract until the end of the season hoping to play every week after injury problems at former club Hull City.
Neilson explained that he does not want to distract the player just now but plans to hold discussions about a longer stay over the next few weeks.
“We are really pleased with him. Stephen just wants to get playing consistently and it's something we will definitely speak about in the coming weeks. He has been fantastic since day one,” said Neilson
"When he came in the door, he said: 'I just want to play every week, see how I do and take it from there.'
"We will definitely speak to him at some point but I just want him to focus on his football at the moment. We have some big games coming up.
“What I don't want to do is cloud it at all for him. He has been out for a long period of time. He was injured quite considerably at Hull and a wee bit at Swansea as well.
“He just wanted to be back playing week in and week out. It's just a flat one-year deal and he's been great so I would like to try and get some sort of agreement in place.”
Kingsley played with Neilson at Falkirk during season 2012/13 and the manager is not surprised at how the recent signing has performed back in Scotland.
He believes there is scope for further improvement in the months ahead as Hearts strive for a quick return to the Premiership.
“I knew his quality from his time at Falkirk. He's played for Scotland, he's played in the Premier League in England and in the Championship. He is a top player,” explained Neilson.
"It was just whether he would be able to play every week. I think he's still getting there and I feel there's still more to come from him.”
Neilson is preparing his players to face Alloa Athletic for the second time in four days. He will again be without winger Josh Ginnelly for Saturday’s Betfred Cup last-16 tie.
The astroturf pitch at the Indodrill Stadium will, to some extent, influence his team selection after Tuesday’s 3-0 league win against the same opponents at Tynecastle.
“A couple of them would prefer not to play on an astro so we will make some changes on that side but the rest of them will be fine. Ginnelly will miss out, which is disappointing, but we just hope to get him back as soon as we can,” said Neilson.
With Hearts already in the Scottish Cup final and coveting promotion, the League Cup is another priority.
“We are two games from Hampden. I think it's really important for us to continue aiming for these big tournaments and go as far as we can,” added the manager.
“We had a good result on Tuesday night but it's a totally different environment down there. It's a different surface, they are used to it so we have to be ready.”