The Englishman was left coughing up blood following a collision with Ross County's Mihael Kovacevic in Killie's 1-0 win in Dingwall last month.
The 24-year-old punctured a lung and cracked four ribs in the accidental clash and has been ruled out for the rest of the Clydesdale Bank Premier League season, but Kilmarnock boss Kenny Shiels wants to keep hold of the Crystal Palace trainee and has offered him a three-year deal.
Dayton, however, says he will only discuss terms once he is back on his feet.
He told Press Association Sport: "I'm out of contract in the summer but right now I'm just trying to sort out this injury first.
"The club have offered me a new deal and we are in talks at the moment but for me it's just about sorting out this injury before I decide anything.
"It's hard for me to get around with the injury and this is the sort of thing that's better done face to face.
"If things can be sorted out with the contract, I can't see why I wouldn't want to stay at Kilmarnock, but we'll just have to see how things go."
Dayton originally hoped to return to action before the end of the season but admits time has run out for his recovery.
He said: "The ribs are coming along. They are still a bit sore, a bit bruised, but they are a lot better than when I first broke them. The timescale hasn't changed, though, and I'm still out for the season. But I should be back for pre-season which is always an important time of year."