TMZ Sports has learned the infamous jacket Reed wore during the "Willis Reed Game" ... as he limped onto the Madison Square Garden court for the deciding contest against the Los Angeles Lakers will soon go to the highest bidder.

Remember, Reed tore his thigh muscle in Game 5 of the series against L.A., and missed Game 6 because of the serious injury.

With Willis out, Wilt Chamberlain went off, dominating the Knicks, and forcing a deciding game 7.

The Knicks appeared to be in big trouble ... as almost no one expected Reed to play in game 7, despite the Knicks being just 4 quarters from a title.

But, after receiving medical treatment on his torn thigh, Reed somehow hobbled onto the court at MSG ... and fans couldn't believe it.

Reed, who was severely limited during the game, scored just 4 points and collected 3 rebounds ... but it was about more than just his contribution to the box score.

Willis, now a College and Basketball Hall of Famer, inspired his teammates with his heroics, leading the Knicks to a game 7 win and an NBA championship.

Fellow Knicks legend Walt "Clyde" Frazier scored 36 points, and dished 19 assists in one of the finest game 7 performances of all-time.

Throughout the historic night, from the time he ran on the court to while he sat on the bench and watched the game, Reed wore his NYK warmup.

Now, that jacket is soon to be available at Grey Flannel Auctions ... with a starting bid of $10K.

The closing price will be significantly more money.

GFA tells us the warmup jacket has been photo-matched to ensure its authenticity. Experts examined several images of Willis in the jacket, including stills from his interview with legendary broadcaster Howard Cosell during the team's championship celebration.

The size "48" and "L" jacket has the Knicks' "NY" logo in orange and blue on the left chest ... and the words "New York" are on the back in the same colors as the front.

Reed's iconic jacket officially goes up for auction on May 16.