Scotland coach Andy Robinson has long been looking for a creative inside centre, with Horne and Edinburgh's Matt Scott among the options to line-up in the number 12 jersey against the All Blacks.
"I'll be striving to put my hand up for selection," Horne said.
"Hopefully I'll have a good training camp and leave the rest to the coaches. If they see fit I'll jump at the chance.
"Matt Scott's another fantastic player. He's got a great ability to pass the ball and a lot of creative talent. It will be cool to go up against him.
"It will be a good camp to test myself."
Another uncapped player in the Scotland squad is Edinburgh lock Grant Gilchrist, who spent the summer of 2011 playing in New Zealand.
"It's been key to my development," Gilchrist told the Scotland Rugby Union's website.
"I feel like I learnt a lot and came back a much better rugby player, got my chance with Edinburgh and managed to take it.
"Playing for Scotland's been my dream since I was a little boy. Any game would be brilliant, but to play against the world champions at home would be absolutely amazing."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.