Williams, a tourist with the Lions in 2005 and 2009, equalled Edwards' feat of 18 Championship tries with his thrilling match-winner in the victory over Scotland a fortnight ago.
In the midst of the dramatic climax at the Millennium Stadium, Williams' last-gasp try also took him past fellow Lions wing Rory Underwood to become the best Test finisher in the northern hemisphere.
Next up for Wales is a historic Friday night showdown with France in Cardiff and birthday boy Williams wants to celebrate in style by re-writing his name in the history books and ending Lions legend Edwards' 32-year-old record.
"I love scoring tries and that's the main reason why I'm in the squad," said Williams, who turns 33 on Friday.
"It will be a massive honour to beat Gareth Edwards' championship record.
"It would be great because he is a legend of the game. In fact I'm a friend of his now - it's absolutely crazy.
"I have enjoyed scoring tries ever since I was a kid and I am football's equivalent of a striker.
"It is what I am here to do and I'm sure Warren Gatland and the coaches want me to keep going. Maybe I'm greedy but I try to pop up everywhere and then reap the rewards by being on the end of that final pass.
"But I try not to think too much about the records. Of course, I want to continue and score more tries for Wales and eventually get up to the likes of David Campese."
Wales' record try-scorer lies 13 scores behind the former Australian star after his 49 touchdowns for Wales and a brace for the Lions.
Williams has scored an incredible 20 tries in his last 23 appearances for Wales with a remarkable strike-rate (87 per cent) which is even superior to Chelsea star Didier Drogba who has netted 19 times in 22 Premier League games this season (86 per cent).