Bothroyd is in Fabio Capello's squad for the friendly against France.
Cardiff boss Dave Jones said: "There are some quality players who play in the Championship. What they have to do is then show they can step up to the next level.
"I believe Jay Bothroyd can and that's why I recommended him for selection to the England team.
"He's having an excellent season for us, I think he finds himself at home with a club that really believes in him. We are the first club that have ever offered him a contract extension."