Thompson, 27, is a long shot to make the Yankees' roster this spring. He is batting .364 through Thursday's action, but with the club projecting to carry just four outfielders, Thompson believes he is destined to begin the season at Triple-A Scranton/Wilkes-Barre.
Thompson was in the Major Leagues three times last season, batting .300 with one home run across 19 games.
His best chance of returning to the Bronx, Thompson said, would be if the Yankees decide they want to carry a fifth outfielder -- and for that player to be a right-handed batter. If they want a left-handed batter, the call would likely go to fellow 40-man roster member Kevin Reese.
Thompson said he can't worry too much about it. Last spring -- when he was absorbing tutelage from both Williams and Gary Sheffield -- Thompson was an even longer shot. He can feel the progress.
Through an intensive workout program that he maintains partly for work, partly for fun, the well-built outfielder vows to be prepared whenever the call comes.
"Everybody knows what's going to happen," Thompson said. "They might play guys here and there, but there's really not much I can do. I've just got to go out there and perform."
Admitting that he followed Williams' ongoing situation with the club closely, Thompson entered the spring with high hopes. The Yankees were unwilling to offer the 38-year-old Williams a Major League contract, instead issuing a standing non-roster invitation to camp.
After telling reporters (but not the Yankees, officially) that he did not intend to accept the invitation, Williams is generally believed to be working out near his Armonk, N.Y., home, remaining in baseball shape for a telephone call that may or may not come.
The situation put Thompson in an undecided situation. Did he want to see Williams at Legends Field? Of course. But at the expense of his own big-league opportunities?
"I mean, he's an icon of the New York Yankees, so you're not hoping he doesn't [report]," Thompson said. "You're hoping he comes back, but it benefits you if he doesn't. I wanted him to be here, because I learned a lot from him. It's kind of a lose-lose situation, I guess you could say."
Maybe so, but now that camp is under way, most have stopped waiting for the morning when Williams walks through the Legends Field clubhouse doors, drops his bags in manager Joe Torre's office and asks to see where he's batting in the lineup.
The Yankees have moved on, with Thompson, Melky Cabrera and Reese absorbing many of the outfield at-bats; more are available to go around while Bobby Abreu rehabilitates his strained oblique muscle.
For Thompson, Williams' decision to remain in New York has created what the outfielder feels is a "great opportunity." But it also means a spring without Williams' presence and guidance.
Thompson recalls one instance in which the Yankees' outfielders were practicing going over their shoulders to track down deep drives in workouts.
"OK, Kevin, this is the angle I'm going to take," Williams would say. "You take this exact angle."
A crack and a catch later, Williams would flip the ball back to the infield, and sure enough, so would Thompson. Some of the techniques and nuances instructed by No. 51 last spring are still being used on a daily basis by No. 27.
"I don't have to cover the whole field," Thompson said. "He showed me how to just cover one section of the outfield, and it takes so much pressure off you. You want to catch everything, and you just can't do it.
"Any time you can make the game simpler like that, in an instant, you're grateful for that. Bernie helped me greatly."