The 28-year-old winger has already fulfilled one ambition - playing for Wales - and now hopes to achieve another with the Lions.
"As a child the only real dream you have is to play for Wales and I have been lucky to do that. The Lions is a new dream for me," Williams said.
"But I'm not going to start worrying about whether I'm getting picked or not.
"I certainly would like to go and it would be totally amazing. It would be a great trip and to be ranked amongst 40-odd of the best players in the British Isles would be a privilege.
"But I'm going to worry about that when the time comes really. Luckily I've had a few other things to worry about like the Grand Slam," he added in the Western Mail.
"So that's kept my head off worrying about what's going to happen in the summer really.
"Until my name is down on that squad sheet in Sir Clive's handwriting, I'm not going to worry about it."