The players became close friends at Rugby Park before Kyle departed on freedom of contract to sign a two-year deal with Hearts. He has implored Bryson to follow him to Edinburgh to accelerate his career development.
Hearts manager Jim Jefferies lured Bryson to Kilmarnock from Clyde in 2007 and considers the 23-year-old a priority signing for next season. With Darren Barr and Kyle both in place, Jefferies is firmly focused on recruiting Bryson, although negotiations with Kilmarnock have laboured as the clubs have yet to agree a fee for a player whose contract runs until June 2012.
Hearts value Bryson at around 300,000, while Kilmarnock believe he is worth significantly more. Kyle is keen for negotiations to progress to ensure he is reunited with Bryson for next season.
"I'd love Craig Bryson to come here," he said. "He's my friend, although I haven't texted him yet to tell him Hearts is a good club. Craig has been talked about in Scottish football for the last season or two, and rightly so because he's a fantastic little midfielder.
"He has great energy, he's a box-to-box player, although more attacking than defending. He's got class, skill and ability and he's got a great range of passing. He could get in any team but Kilmarnock will be desperate to hold on to him because he'll probably be their most prized asset. It will be difficult to lure him away but if Jim could get him it would be a magnificent coup and would benefit Hearts immensely.
"The transfer market is a tricky thing. Jim has plenty experience of it, the owners of the club will try to help Jim as best they can. If Hearts got Craig Bryson, I would welcome him and I'm sure the fans would as well."