Discussions have taken place with several groups after Peace made the decision earlier in the year to offer up his 88 per cent share of the Baggies as he “considered strategic options for the future development and legacy of the club”.
Speculation has linked a Chinese consortium with the club but there has been no confirmation of the identity of the party to whom exclusivity has been granted.
In a statement West Brom said: “This process should be completed by the end of this month and, in the meantime, the club wishes to assure supporters preparations for the new season will remain unaffected.
“The chairman, head coach Tony Pulis, chief executive Mark Jenkins and Richard Garlick, the director of football administration, have met to discuss and progress future transfer targets.
“They remain in constant dialogue over the re-shaping of the first-team squad for the 2015-16 Barclays Premier League campaign.”
Peace, who has been chairman since 2003, reportedly values the club at between #150million and #200million.