The Scot goes into the clay-court Grand Slam event hoping to reach the second week for the first time.
But if things go his way, the world No 3 could even overtake former world No 1 and five-time Wimbledon champion Federer in the rankings.
Murray, who faces Argentina's Juan Ignacio Chela in today's first round, admitted: "That's what I want to try to do here.
"From the start of the tournament, I've obviously got a lot to gain and unless Federer wins the tournament, he's going to lose points. I could do it here at this tournament."
Unless Federer loses in the first week, Murray needs to reach the semi-finals in Paris to overtake him. Just 12 months ago, Murray was ranked at No 12 and had never reached a Grand Slam quarter-final.
But, after making the last eight at Wimbledon, he went on a stunning run and reached the final of the US Open.
Six tournament victories since August have lifted Murray above Novak Djokovic to No 3 - the highest ranking by any Brit since the system was introduced in 1973.
But passing Federer, who is just one short of the record of 14 Grand Slam titles held by Pete Sampras, would be something extra-special.
Murray added: "When you get closer to doing something like that - to overtake Roger Federer in the rankings - it's big news.
"It's not like it happens very often. Rafael Nadal took 4½ years before he did it. But I just need to concentrate on my own game and not worry about what he does."
Murray reached the semi-finals of the clay- court Masters event in Monte Carlo in early April and then the quarter-final of the Madrid Masters nine days ago.
He admits he still has a long way to go before he rivals Nadal on clay, but is now rated as one of the favourites for the event.
Yet Murray said: "I try and block out that sort of stuff. At Wimbledon everyone says there is so much pressure on me because of all the people watching so it should be easier here.
"But I view all the Grand Slams the same. I know I have to play my very best tennis from the start here, which I don't necessarily have to do on the other courts."
In the women's event, British No 1 Anne Keothavong faces an enormous task against top seed Dinara Safina of Russia in the first round.
Mel South takes on Michelle Larcher De Brito of Portugal. And Katie O'Brien yesterday became the third British woman in the main draw as a lucky loser.
She replaces injured sixth seed Vera Zvonareva and will play Belarussian Olga Govortsova in the opener.
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