The 29-year old striker returned to Scottish football with Killie in February following failed stints in England with Middlesbrough and Nottingham Forest, in Turkey with Eskisehirspor and in the USA with Portland Timbers and scored three goals in eight league outings for the club he made his name with.
Now he is attracting interest from Hearts but admits he is eager to stay put at Rugby Park.
"I've enjoyed being back and it ticks a lot of boxes for me," he said.
"I want to speak to Kilmarnock and that will probably happen this week or next. The family is settled and if you're happy at home, you're happy on the park. I'm probably swaying more towards staying at Killie.
"Lockey (Hearts boss Gary Locke) has phoned me a couple of times to see if I'd be interested in going to Hearts.
"And at this moment I'm not ruling out anything. Hearts are a good club.
"I want to enjoy a break with my family. I know I need to have something sorted by the time I come back my holidays."