The Hammers manager, who will spend a second night at the Royal London Hospital was admitted after complaining of pains in his chest after the 1-0 win over Boro on Easter Monday.
However, a statement on the club's official website said: "We are pleased to confirm that despite numerous press reports, the nature of the problem is not related to a heart condition.
"The Roeder family would like to thank supporters and people within the football world who have sent goodwill messages.
"At this time, we would ask that people respect the privacy of the family.
"No further statement will be made until the results of the tests are available."