Lady Bracewell-Smith, who holds nearly 16% of the club's shares, has appointed bankers to find a buyer for the shares, according to the Evening Standard.
Russian billionaire Alisher Usmanov and Stan Kroenke have long been fighting for control of the club and if either bought a notable amount of Bracewell-Smith's stock, it would trigger a formal takeover bid.
Kroenke reportedly needs as few as 10 shares to reach the threshold. He holds 29.9% of shares, the highest figure allowed by Stock Exchange rules without a takeover bid.
Usmanov's Red and White Holdings have 26%.
Bracewell Smith could get £80million if she sells out altogether and is understood to have hired Blackstone, a US group, to find a buyer, a move which could imply she is not intending to sell to fellow director Kroenke.
The decision is something of a surprise as Bracewell-Smith has often insisted she has no intention of selling her stake.
Arsenal offered no comment on the report.