Reid, who is out of contract at the end of the season, had been tipped to make a move away from Upton Park.
But the ESPN FC website has quoted sources as saying the 26 year-old defender has agreed to a new long-term with the club.
Earlier this week, West Ham manager Sam Allardyce said Reid was still considering his options and had yet to decide on "an exceptionally good offer" the Hammers had put on the table.
Since joining from Danish side FC Midtjylland in 2010, Reid has become a key member of the West Ham line-up.
He started in their 1-0 home defeat to league leader Chelsea on Thursday (AEDT), but had to go off in the sixth minute because of a muscle injury.
