The tiny but symbolic stake stemmed from support offered by the Glasgow club to Arsenal when they fell on hard times early in the 20th century.
Rangers are now facing their own financial crisis, having gone into administration last week over unpaid taxes and with a potentially ruinous second tax bill hanging over them.
Usmanov bought the 16 shares last year through the market, a source close to the businessman said on Wednesday .
Usmanov has said he is prepared to pay up to 14,000 pounds ($22,100) per share as he seeks to take his stake in Arsenal from some 27 percent last May to 30 percent.
American Stan Kroenke owns a majority stake in Arsenal and Usmanov has been steadily building up his holding in the club through his Red & White vehicle as part of his opposition to Kroenke's takeover.
Arsenal moved from their original base in Woolwich, south London, to north London in 1913 because of their financial problems and have gone on to become one of English soccer's most successful clubs.