Adam Partridge Auctioneers have put an estimate of up to £3,000 for the rare item of sporting memorabilia. Bids are already into four figures.
The badge - and the blazer - were given by Sir Tom to one of his four sisters for her son. The badge was eventually passed down to a niece who has now put it up for auction.
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The auction catalogue says: "The vendor is his niece, she remembers Sir Tom giving his first blazer to his sister to give to his nephew who is in need of a blazer.
" 'You better take the badge off or I will be in trouble, I don't need this anymore because they have given me a new blazer.’
"The vendor's mother removed the badge, wrapped it up and put it away. It was recently rediscovered and framed."
Also in the frame is a photograph of Sir Tom in his England playing kit and signed: "Best wishes to Madge, Tom Finney." Madge was his eldest sister.
And there is also a shot of him in army uniform from his war service.
Finney made his England debut on September 28, 1946, just four weeks after he had made his professional debut in a Football League match at Deepdale against Leeds United in which he scored once and made two others in a 3-2 win for Preston.
On his international debut for England he also scored one of the goals in a 7-2 victory at Windsor Park, Belfast. He later described it as his "proudest day as a footballer."
He went on to play for his country 76 times, scoring 30 goals. In October 1958 he again scored to become the country's all-time top scorer - a record which lasted just two weeks.
His good pal Nat Lofthouse also reached 30 goals to share the title, only for Bobby Charlton to surpass them both in October 1963.