Tom Lehman is currently 54th in the world rankings, Mark Calcavecchia 57th, Paul Azinger 68th, Jesper Parnevik 83rd and Greg Norman way down in 118th with only the top 50 being invited.
Says former US PGA champion Azinger: "Obviously, it's on my mind, but if I don't play good enough to get in the Masters based on that world ranking, I don't deserve to play. I'm not really thinking about it too much.
"I just want to start making good, solid contact with my driver again. It's been really frustrating. I start every single hole behind the 8-ball because I'm scrambling. I was probably the least accurate driver on Tour last year.
"Normally, I'm between 50th and 100th in accuracy off the tee," Azinger said. "I've never been any better, or expect to be. But I expect to be that good. I don't expect to be 150th, or whatever I ended up. It's horrendous."
Lehman, winner of The Open Championship at Lytham in 1996, had his worst PGA Tour season, finishing 74th on the money list.
"My feeling is, I played just about as poorly as I possibly could play last year," Lehman said. "I don't like finishing 70th on the money list and not having a chance to win. I was so inconsistent. I'm not surprised at all that I dropped where I dropped to.
"I've been home practising a lot, having developed a few bad swing habits from playing with a separated right shoulder for six months in 1999 before having surgery.
"I have a good understanding of what has been making me hit it so poorly. It's just a matter of fixing it, which isn't always that easy.
"So it's important for me to spend a lot of time between now and the Hawaiian Open so that I do get off to a good start. If I don't, my chances of playing Augusta are going to be pretty slim and it would be the end of a nice run."
Among the Europeans making their debut in Augusta are Justin Rose and Spain’s Amateur champion Alejandro Larrazabal.
Top stars still to qualify for Augusta